Vasileios Rakopoulos

Measurements of Isomeric YieldRatios of Proton-Induced Fission

of natU and natTh

at the IGISOL-JYFLTRAP facility

AbstractThis thesis presents the measurements of isomeric yield ratios of fission products in 25 MeVproton-induced fission of natU and natTh, performed at the Ion Guide Isotope Separator On-Line(IGISOL) facility at the University of Jyväskylä.

Knowledge of the relative intensities of metastable states produced in fission is of importancefor various fields of nuclear physics, both fundamental and applied. The angular momentumof fission fragments is regarded as an important quantity in order to understand the fissionmechanism because it can provide information on the scission configuration. One of the meansto deduce the angular momentum of highly excited nuclei is by determining the yield ratio oflow lying isomeric states.

Isomeric yield ratios are also important themselves for simulations of processes such as ther-process, which is believed to be terminated by the fission of very neutron-rich heavy nuclei,and the neutronics and decay heat of nuclear reactors. In addition, proper simulation of the effectof delayed neutrons in a reactor requires accurate knowledge of the population of isomeric states,since the β -delayed neutron emission probability from the isomeric state can be an order ofmagnitude different from that of the ground state.

The measurements were performed from 2010 to 2014, both at IGISOL-3 and at the re-cently upgraded and relocated IGISOL-4 facility. With the IGISOL method short-lived fissionproduct yields can be measured and, by employing the high resolving power of the Penningtrap JYFLTRAP, isomeric states separated by a few hundred keV from the ground state can beobserved. Thus, a direct determination of the isomeric yield ratios by means of ion counting,registering the products in less than a second after their production has been accomplished forthe first time. In addition, γ-spectroscopy was employed in order to verify the consistency of theexperimental method.

Isomeric yield ratios of fission products were measured in a wide mass range (A = 81 to130) for 25 MeV protons on natU and natTh. Specifically, six isomeric pairs (81Ge, 96Y, 97Y,97Nb, 128Sn and 130Sn) with suitable half-lives were measured and indications of a dependenceof the production rate on the fissioning system were observed. A 25 MeV proton beam wasselected as there are experimental data available in the literature, determined by means of γ-rayspectroscopy, so that a comparison of the results could be performed.

"survive another winter"to Katerina and Elias-Sebastian

List of papers

List of papers is not included in this thesis.

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 A (brief) introduction to fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Isomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 The importance of isomeric yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Fission yields measurements techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Experimental Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1 The IGISOL technique combined with JYFLTRAP . . . . . . . . . . . . . . . . . . . . 172.2 Description of experimental elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 The fission ion guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Mass separator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.3 Radio-Frequency cooler and buncher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.4 Isobaric purification with JYFLTRAP . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.5 Timing Structure of the measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Chemical effects of IGISOL and JYFLTRAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Penning Trap Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1.1 Time of flight selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.2 Peak intensity determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.3 Corrections due to radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 γ-spectroscopy Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Efficiency calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.2 Decay corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.3 Transport efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.4 Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.1 Presentation of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Discussion and comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.1 Mass 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.2 Mass 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.3 Mass 97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.4 Mass 128 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.5 Mass 130 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

List of Figures

Fig. 1.1: Nucleus deformation in terms of a liquid drop model . . . . . . . . . . . . . . . . . . . 4Fig. 1.2: Potential energy surface of deforming nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Fig. 1.3: Double-humped fission barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Fig. 1.4: Time scale of fission fragments de-excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Fig. 1.5: Decay paths of nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Fig. 1.6: De-excitation of the fission fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Fig. 1.7: Decay scheme of mass chain A=115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Fig. 2.1: IGISOL and JYFLTRAP facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Fig. 2.2: The fission ion guide at IGISOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Fig. 2.3: Ion’s trajectory in the Penning Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Fig. 2.4: Conversion of the ion’s motion in the trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Fig. 2.5: Timing structure of the measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Fig. 3.1: Time of flight distribution of mass A=96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Fig. 3.2: Mass spectrum without and with TOF gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Fig. 3.3: Frequency distribution of mass A=96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Fig. 3.4: γ-ray spectrum of mass A=128 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Fig. 3.5: HPGe intrinsic efficiency curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Fig. 4.1: Isomeric yield ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Fig. 4.2: Frequency spectrum for mass A=81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Fig. 4.3: γ-ray spectrum for mass A=81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Fig. 4.4: The case of multiple results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Fig. 4.5: Investigation of the IYR dependence on the fissioning system . . . 51Fig. 4.6: IYR as a function of the spin difference of the states . . . . . . . . . . . . . . . . . . 52

Preface

This thesis reports on the experimentally deduced isomeric yield ratios fromproton-induced fission on natU and natTh. All the measurements were per-formed at the IGISOL-JYFLTRAP facility at the University of Jyväskylä overa span of four years, from April 2010 to May 2014.

This work was accomplished as part of the collaboration between UppsalaUniversity and the University of Jyväskylä that aims at high precision measure-ments of fission yields. Since the fission yields are an important characteristicof the fission process, a brief introduction of the latter is attempted in Chap-ter 1, where a description of the time evolution of the fission and a definitionof the fission yields are given. In addition, the importance of the knowledge ofthe population of the isomeric states for both fundamental and applied physicsis emphasised, as motivation for the present work. At the end of the chapterdifferent techniques of measuring fission yields are described.

During this period of four years, a lot have changed at the IGISOL facilitysince a major upgrade was realised, both in the IGISOL and JYFLTRAP fa-cilities. Chapter 2 gives an overview of the renewed facility, highlighting themost important elements along the beam line.

In Chapter 3, the analysis procedure which was developed and followed inorder to deduce the yield ratios of the acquired data is presented. The resultsof this analysis are presented in Chapter 4, together with some remarks thatcould be drawn as an outcome from the comparison of the results with eachother and with experimental data available in the literature.

Last, in Chapter 4 the conclusions of this study are summarised, and someplans for the future are mentioned as well. I was involved in one of the per-formed experiment, in April 2014. My contribution to this sequence of mea-surements was to develop the analysis routine, deduce the isomeric yield ratiosand compare the obtained results.

1

1. Introduction

1.1 A (brief) introduction to fissionFission was first observed experimentally in January 1939 by Otto Hahn andFritz Strassmann [1]. The reaction in which fission was studied was neutron-induced fission of Uranium. In the process a heavy nucleus decays into twofragments of comparable mass. It was first discussed quantitatively by LiseMeitner and Otto Frisch [2], who discussed the process in terms of a liquiddrop, which becomes deformed and which beyond a critical deformation isbreaking apart into two pieces, the fission fragments. The same year, N. Bohrand J. A. Wheeler in their prominent work gave an extended theoretical de-scription of fission [3].

The mechanism of fission is a very complicated process and we are still farfrom a detailed understanding. That’s why although fission induced by neu-trons in the actinides is perhaps the most studied reaction of nuclear physics,a complete picture of the process is still lacking. From the perspective of theliquid drop model (LDM) description, a neutron that enters into the actinidetarget adds excitation energy to the compound nucleus, resulting in shape de-formations and change in the potential energy, which increases above the levelof the ground state. In the landscape of deformation, there is a critical defor-mation of no return, which is called the saddle point, as can be seen in Fig. 1.1.Afterwards, with further deformation, a situation is reached where the neckjoining the two nascent fragments is no longer stable but is breaking apart.The snapping of the neck is called scission. Thereafter, the fragments1 arecreated in general with unequal masses. The available energy in fission is ap-proximately 200 MeV and is shared between the total kinetic energy (TKE)and total excitation energy (TXE) of the fragments. In order to de-excite, thefragments will emit neutrons (secondary prompt neutrons) and the process iscompleted with γ-rays emission.

The binding energy (B) of a nucleus can be described by the semi-empiricalformula of Bethe-Weizsäcker, based on the liquid drop model (LDM) [4]:

B = ανA−αsA2/3−αcZ(Z−1)A−1/3−αsym(A−2Z)2A−1 +δ (1.1)

• the first term stands for the volume term, which increases with increasingnumber of nucleons. It is referred to as the volume energy (Eν ) and itis the most important factor of the formula, especially for the lighternuclei.

1The formation of two fragments (binary fission) is much more likely than the formation of three(ternary fission), which occurs with a low probability of only a few events per 1000 fissions.

3

n

Fragment I Fragment II

Saddle

Scission

secondary neutrons

Fig. 1.1. Visualisation of the nucleus deformation in terms of a liquid drop.

• the second term gives the surface energy (Es), which describes the factthat nucleons on the surface have less neighbours to interact with, result-ing in a decrease in the binding energy.

• the third term, the Coulomb term (Ec), expresses the repulsive interac-tions between the protons in the nucleus due to the Coulomb force, andit contributes to the split of the nucleus. In cases, like fission, wherethe nucleus deforms considerably, this might become an important termbecause the Coulomb repulsion might overcome the short range of thestrong nuclear force.

• the fourth term, which is called the symmetry energy (Esym), describesthe tendency of the nucleus to become symmetric in protons and neu-trons in order to be stable. This term is more important for light nuclei,since for the heavier ones the increase in Coulomb repulsion requiresadditional neutrons for nuclear stability.

• the last term, which is called the pairing term (Ep), expresses the ten-dency of nucleons to couple pairwise in order to form stable configura-tions. Specifically this term does not contribute when A = odd (odd Zand even N and vice versa), δ = 0. However the relatively high stabil-ity of even-even nuclei is taken into account by a positive contribution(+δ ) to the total binding energy EB of the nucleus, and the relatively lowstability of odd-odd nuclei by a negative contribution (−δ ).

4

The surface and the Coulomb energy terms in Eq. 1.1 are the only ones whichare affected when a liquid drop becomes deformed. Specifically, the surfaceenergy term is smaller for a sphere, but any deformation away from this shapeis associated with larger potential energy from this effect. The Coulomb en-ergy term is decreased with a deformed nucleus, because of the larger averageseparation between the charge elements. A radius vector R(θ ) of the nucleuscan describe the small axially symmetric deformation:

R(θ) = R0[1+α2 P2 cos(θ)] (1.2)

where θ is the angle of the radius vector, α2 is a coefficient that describes theamount of the deformation, R0 is the radius of the non deformed nucleus andP2 is the second order Legendre polynomial [5].

The surface (Es) and the Coulomb (Ec) energies for small deformations,were calculated by Bohr and Wheeler:

Es = E0s (1+25

a22) and Ec = E0c (1−

15

a22) (1.3)

where E0s and E0c are the surface and Coulomb energies respectively without

any deformation. In order for a spherical nucleus to be stable against deforma-tion the decrease in Coulomb energy ∆Ec=- 15 α

22 E

0c must be smaller than the

increase in the surface energy ∆Es= 25 α22 E

0s . The drop will become unstable

when the absolute values of the aforementioned terms equal each other, whenE0c=2E

0s . Thus, as introduced by Bohr and Wheeler, the notion of the fissility

x can be defined:

x =E0c

2E0s(1.4)

For x less than unity the nuclei are stable, while for x bigger than unity therewill be no potential energy barrier to inhibit spontaneous fission of the drop.

In order to describe the large deformations that are encountered on the topof the fission barrier, higher order polynomials must be included in Eq. 1.2:

R(θ) = (R0/λ )[1+ ∑n=1

αn Pn cos(θ)] (1.5)

where the parameter λ ensures that the volume remains constant.The potential energy of the deformation is increasing as expected for small

deformation, as can be seen in Fig. 1.2. There is though, a crucial point whichis reached for specific values of the deformation parameters. This point iscalled saddle, and a fissioning nucleus moving along the path of deformationhas to overcome the potential barrier at this point, the fission barrier B f . Theheight of this fission barrier for the actinides is about 6 MeV above the groundstate. Beyond this, a path of minimum energy slopes downwards until thenucleus is breaking apart at scission [6].

5

Ener

gy

Sn

Deformation

Bf

En

E*

saddle point

scission point

Fig. 1.2. The potential energy as a function of the deformation of a nucleus. The fissionbarrier (B f ), as classically approached by the LDM model with a single humped barrier,is also noted. On the left side the neutron separation energy (Sn) and the additionalexcitation energy, added to the compound nucleus from the extra neutron, appear aswell. On the top of the figure, the deformation of the nucleus from spherical shape toscission point is illustrated.

The addition of a neutron to the target nucleus contributes to the bindingenergy of the formed compound nucleus, so that the latter might excite abovethe fission barrier, as illustrated in Fig. 1.2. The amount of excitation energywhich needs to be added to the system in order to overcome the fission barrieris strongly case dependent. Nuclei with even mass number A, such as 238U,exhibit a higher fission barrier than the energy required to separate a neutron(neutron separation energy), Sn, so more energy from the incident particle isrequired in order to fission. This happens because the extra neutron will notbe paired to the nucleus, as all nucleons are already in pairs, so extra energyis needed for the compound nucleus 239U to undergo fission. For 238U, theneutron separation energy and the fission barrier of the formed compound nu-cleus 239U∗ are Sn = 4.8 MeV and B f = 6.3 MeV respectively. On the otherhand, nuclei with odd mass, such as 235U which is very well studied for itsuse in nuclear reactors, exhibit a neutron separation energy higher than theirfission barrier. That means that the extra neutron will readily pair with anothernucleon, so that the excitation energy will increase above the fission barrier.

6

For 235U, the neutron separation energy and the fission barrier of the formedcompound nucleus 236U∗ are Sn = 6.5 MeV and B f = 5.6 MeV respectively.

The simple liquid drop model, although it describes the general propertiesof the fission process relatively well, has certain limitations when it is calledto explain experimental results. For example, it fails to explain the two dis-tinct modes of symmetric and asymmetric mass division in fission, which wassuggested from experiments. Maria G. Mayer, in her work in 1948, traced theasymmetric fission back to nuclear shell effects, in particular to the stabilisinginfluence of the 50 proton shell and the 82 neutron shell that coincide in thespherical doubly magic 132Sn [7]. Moreover, it’s not possible to predict theisomeric fission with the single fission barrier of the LDM description. Shelleffects "corrections" were introduced to the liquid drop model by Strutisky [8],thus all the processes that could not be explained by the single-humped modelcould be attributed to shell effects.

Ener

gy

Deformation

Spontaneous Fission

Isomeric Fission

Normal Fission

Mass Distribution

εI εII

I

II

EAEB

Fig. 1.3. Illustration of the double-humped fission barrier as introduced by shellcorrections. Humps at A and B result in minima in potential energy at deformation ofεI and εII . States in these wells are designated class I and class II, respectively.

In Fig. 1.3, the "shell-corrected" description of the fission process is visu-alised, where it can be noticed that the fission barrier becomes double-humped,instead of single. On the top of the same figure the different stages of theshape deformation of the nucleus along the fission path are visualised. As canbe seen, the shape of the compound nucleus is already deformed in the ground

7

state, which lies in the first minimum and it is designated as εI in Fig. 1.3.The second minimum, designated as εII , can explain the isomeric fission. Theshape of the nucleus in this second barrier well is elongated due to repulsionof the number of protons. It has a higher energy than the ground state, so it ismetastable. In this case, the isomerism is observed due to the difference in theshape of the nucleus, and not to be confused with the spin isomers, produceddue to the differences in the spins of the states, and measured in the presentwork. The nucleus is trapped into retaining its elongated shape since its energyis not sufficient to surmount either barrier. Although the decay of the nucleusis not possible with the classical approach, since its energy is below the fissionbarrier, it still may occur by tunnelling through the barrier according to quan-tum mechanics. Actually, this can happen both ways. It can tunnel back to itsmore spherical ground state by emitting a γ-ray, as an ordinary nuclear isomer,leaving its identity isotopically unchanged. It can also tunnel to the other di-rection, by producing two separate fragments by fission. Spontaneous fissionmay occur when the nucleus is on the ground state and tunnel through thewhole fission barrier, without needing any additional excitation energy from aparticle.

Between the two barrier wells, discrete excited states exist (referred to asclass-I and class-II), which become less resolved the higher excitation reached,until as always they enter the continuum level densities region, where they areunable to be resolved. The excited states on the saddle points are referred toas "transition states" and they have their characteristic spin and parity.

Time scale of the de-excitation of the fission processA mention explicitly must be done here on the distinction between fissionfragments and products, since this is closely related to the time evolution of thefission process itself. The fission fragments are highly excited so, in order tocool down they emit neutrons and γ-rays. The time scale involved in the fissionprocess is shown in Fig. 1.4. The evaporation times for neutrons are muchshorter than the emission time of γ-rays, so they first de-excite by neutronemission. After prompt neutron emission the "primary" fragments are called"secondary" or just "products" and their remaining excitation energy is belowthe neutron separation energy. The only way for the nucleus to de-excite morethus, is by emitting γ-rays. The transition from neutron to gamma emissionhappens on a time scale of 10−14 s, while the emission of prompt γ-rays maylast for several ms. After this de-excitation process, fission products reachtheir ground states, but they are still too neutron-rich and hence unstable andliable to β−-decay. This decay may last from several ms up to years. Theradioactivity of fission products is part of the activity of fuel remnants fromnuclear power stations. It is worth mentioning that once the saddle has beenpassed the fission process is very fast, while it takes comparatively long timeto evaporate a neutron.

8

Time scale (s): 10-21 10-18 10-14 10-3 t

Fission Fragments Fission Products

10-20

Light charge particlesScission neutrons

saddle to scission

prompt neutrons prompt γ-rays β-decay: β-particles, delayed neutrons, γ-rays and fission

Primary Fragments Secondary Fragments

Fig. 1.4. Time scale in the de-excitation of fission fragment

Definition of fission yieldsMeasurements of the fission observables such as the mass yield distributionsof the fission products can provide important information about the fissionprocess itself, either for fundamental or applied physics. In Fig. 1.5 part of thechart of nuclides is illustrated, where the possible decay paths of each nuclidecan be seen. The β−-decay is denoted with the black arrows and the neutronemission with the red arrows. Based on this figure and the time scale presentedin the previous paragraph the fission products are categorised as follows [9]:

1. Independent fission yields: a measure of the number of atoms of a spe-cific nuclide produced directly in the fission process before any radioac-tive decay.

2. Cumulative fission yields: describes the total number of atoms of a spe-cific nuclide produced directly in fission and after the decay of all of itsprecursors.

3. Total chain yields: expresses the cumulative yield of the last, either sta-ble or long-lived member of an isobaric chain.

4. Mass number yields: is the sum of all independent yields of a particularisobaric chain.

The difference between the total chain yield and the mass number yield emergesfrom the contribution of β -delayed neutrons. The former contains the pro-duced nuclides after the β -delayed neutrons, while the latter does not. If thereis no emission of delayed neutrons, the two yields concur.

1.2 IsomersIn Fig. 1.6 the de-excitation process of the fission fragments is illustrated. Thefragments produced in fission can be characterised by their distribution of ex-citation energy and initial angular momentum. As explained earlier, the highlyexcited fragments first de-excite by emitting prompt neutrons and then promptγ-rays. As long as the excitation of the fragments is high the neutron emissionprevails, until the excitation energy is reduced below the neutron emissionthreshold. Afterwards, the emission of γ-rays prevails, at the beginning withstatistical E1 emission. The change in the angular momentum due to the emis-

9

Prot

on N

umbe

r Z

Neutron Number N

130Te

130Sb

130Sn

130In

131Te

130Cd128Cd

128Sn

129Sb

129Sn

129In

129Cd

131Sb

131Sn

128In 131In

131Cd

132Te

132Sb

132Sn

132In

132Cd

β-

n

Fig. 1.5. In figure the decay paths of part of the chart of nuclides is illustrated. The blackarrows represent β -decay and the red arrows represent the delayed neutron emission.

sion of the prompt neutrons and the statistical γ-rays is small. In the regionclose to the yrast line, non-statistical (mostly E2) photons carry away the re-maining angular momentum. Most of the isomeric states are formed in thisregion.

Isomeric states are metastable states that occur when the angular momen-tum difference between two states is large. Under these circumstances, theelectromagnetic transition probabilities from these states are reduced, becauseof their high multipole order, resulting in an unusually long lifetime, comparedto other excited states. In the shell model picture, these states are formed be-cause major shells are occupied by particles of high angular momentum, whiletheir close in energy sub-shells are occupied by particles of low-angular mo-mentum. Specifically the major shell closures occur at Z, N = 50, 82 and 126particles on the levels 1g9/2, 1h11/2, and 1i13/2 respectively, while the adjacentlower sub-shells are occupied by 2p1/2, 2d3/2 and 3p1/2 [10].

1.3 The importance of isomeric yieldsIsomeric states encompass a wide range of lifetimes due to several reasons:their state transitions occur in various multipole type and order (E3, M3, E4,M4, . . . ), while their decay modes compete between internal conversion and

10

E*

J

E*

E (Yrast)

PrimaryFissionFragments

SecondaryFission Fragments

n n

γγγ

Sn

Statistical γγ

Discrete levels

γ

}Fig. 1.6. Illustration of the de-excitation of the fission fragments first by promptneutrons emission and then by statistical (E1) γ-rays. Afterwards, the emission ofnon-statistical photons takes place to the region close to the yrast line.

β -decay. Similarly, the ground states to which the metastable states will decay,unless a β -decay occur either from these states or from an intermediate lowerlying level along their decay path, exhibit a similar span of lifetimes, frommilliseconds to stability. Thereafter, it becomes evident that a description ofthe time evolution of the excited states must take into account this variationin half-lives where the population of the isomeric states cannot be ignored.In Fig. 1.7 an example of the decay path of mass A=115 is given in order tovisualise how the presence of the metastable states can complicate the decaypath and branching ratios of an isobaric chain. As can be noticed, 115Rh de-cays by β -particle emission to 115Pd. In 115Pd, the isomeric state at 89.2 keVcan decay either by the dominant in this case β -particle emission (probabilityof 92%) to 115Ag or to the ground state by internal conversion with a smallestprobability of 8%. In addition, the isomeric state in 115Ag complicates fur-ther the situation since its de-excitation competes between β -decay (79%) andinternal conversion to the ground state (21%).

As mentioned in the previous section, the fission products are either stableor unstable to β -decay and/or to delayed neutron emission. Unstable prod-ucts can decay to either nuclides where no isomeric states exist, or to speciesoccupying their (stable or not) ground state or their metastable isomeric state.The time development of the energy release in the latter case depends cruciallyon the initial relative populations (branching fractions) between isomeric andground states. For example, in the case of thermal-neutron fission of actinidenuclei, such as 233,235U or 239,241Pu, roughly 800 primary products are formed.Approximately 700 of these products are unstable and about 150 have known

11

115Pd5/2+

115Ag

7/2+

β- : 100%

41.2 keV

β- : 79%

β- : 100%

89.2 keV

β- : 92%

11/2- 50 s

1/2-

25 s

IT: 8%

0 keV

IT: 21%

18.0 s

0 keV20.0 m

115Rh7/2+

β- : 100%

0.99 s 0 keV

Fig. 1.7. Decay scheme of part of the mass chain A=115. The complications that arisein the decay path due to the different decay modes of the metastable states can be seen.The ground states are illustrated with the thick lines, while the isomeric states with thethinner ones.

isomeric states with half-lives τ ≥ 0.1 s [11]. The importance of isomericstates in calculations of fission products decay energy release, such as thedecay heat calculations, is thus clear. In addition, the β -delayed neutron emis-sion probability from the isomeric state can be up to an order of magnitudedifferent from that of the ground state (e.g. 0.33% for 98Y , 3.5% 98mY accord-ing to NuDat2 [12]). Therefore, a proper simulation of the effect of delayedneutrons in the nuclear reactors requires accurate knowledge of the populationof isomeric states in fission.

Moreover, the knowledge of the population of the isomeric states is impor-tant in yield measurements of fission products. In such studies, close-lyingisomeric states to the ground state of a nuclide might create peak multipletsthat are difficult to resolve. Thus, the yields of isomeric and ground states areoften summed together. In order to apply corrections for the population of themetastables states knowledge of their intensity relative to the ground state in-tensity is needed. It is worth mentioning that the shorter the isomer’s half-lifeis compared to the ground state’s lifetime, the more significant the correctionis.

So far the importance of isomeric states to applications has been described.Nevertheless the isomeric yield ratios are important for simulation of pro-cesses such as the astrophysical r-process. The r-process is believed to be

12

terminated by the fission of very neutron rich heavy nuclei, while the fissionfragments return to the r-process path. Furthermore, the neutron capture of thehigh spin isomeric state can be very different compared to the one of the lowspin ground state. Hence, these simulations need as accurate knowledge aspossible of the population of isomeric states. The fissioning systems that ter-minate the r-process are more neutron rich than any of those that can currentlybe reached in the experimental frame, so their yields are estimated based ontheoretical calculations. In order to test the ability of the theories to reproducethe isomeric yield ratios of the fissioning system, they have to be determinedexperimentally.

Besides all the aforementioned reasons for which isomeric yields are impor-tant themselves, they can also be used in fundamental physics, in the effort fora better understanding of the fission process. The angular momentum of thefission fragments can provide better information on the scission configuration.One of the possible means to deduce the angular momentum of the fragmentsis the independent isomeric yield ratio of fission products, which can be usedto study the collective rotational degrees of the fissioning system at the scis-sion configuration. In [13], and the references therein, more information canbe found on the deduction of the root mean square angular momentum of theprimary fragment (Jrms), while in [14] information on the deduction of theproperties of scission configuration can be found. In the first efforts to deducethe Jrms, time consuming radiochemical separation techniques were used, re-sulting in limitation on the isomeric pairs, because these had to be locatedclose to the valley of stability and shielded by stable or long-lived isotopesfrom production via the beta decay of more neutron-rich isotopes. In morerecent works, [15] [16], direct γ-ray counting was employed and the deducedproduction via β -decay is simply subtracted from the total yield.

1.4 Fission yields measurements techniquesThe measurement of fission yields is a complicated process because the fis-sion fragments are not formed in a single way. Therefore several differenttechniques have been developed over the years aiming at measuring the cumu-lative or the independent yield, each one with its own advantages and draw-backs. They can mainly be distinguished in two main categories:

• measurements of stopped fragments.• measurements of unstopped fragments.

The oldest technique in the first category is radiochemical separation ofthe longest lived isotopes of fission products. Then, the activity could be de-termined via β - or γ-spectroscopy. At the beginning, the method was timeconsuming, so it was able to measure only long-lived isotopes. After somedevelopment, short-lived isotopes with a life-time of the order of seconds orless could be identified as well, and even isomers in some cases.

13

Fission products can also be measured by means of mass spectroscopy, mak-ing use of radioactive beams. Specifically with the Isotope Separator On-Line(ISOL) technique, a thick target is irradiated, and the created products are in-troduced to an ion source, where they are ionised. Afterwards the ions aremass separated by means of magnetic separation, resulting in pure ions beams,which can be detected by ion counters. The fission products can also be de-tected by means of γ-spectroscopy, since the β -decay of the products is fol-lowed by γ-ray emission. If products are adequately long-lived so that theirdecay occurs after the mass separation, the unique γ-ray spectrum of each iso-baric chain can be employed. The drawback of this method is that it is slowsince a thick target is used in order to create a sufficient yield of a product.Moreover the universal use of this method is hindered by the limitations thatarise from the use of the ion source. Although in fission a large variety ofnuclides is produced, there is not an ion source that can be used for all of themsince the chemical selectivity of the ion source is governed from the differentionisation properties of the elements.

In order to measure independent fission yields a variant of this techniquehas been developed. Specifically with the Ion Guide Isotope Separation On-Line (IGISOL) technique, a thin target is connected directly in the ion sourceso that the method is fast and ions of all chemical elements can be produced.However, one of the biggest issues of this method is its limited mass resolvingpower, resulting in longer irradiation time in order to overcome this problem.In addition the decay scheme of the most exotic nuclei is not well known insome cases.

Direct measurement of γ-rays can be performed as well in case of veryexotic targets, since with this method a very small amount of the sample isrequired. On the other hand, the data analysis is complicated and accurateknowledge of the decay scheme is necessary. Moreover in the case of indepen-dent yield measurement, the decrease in the irradiation time, results in reducedstatistics and consequently in larger uncertainties.

The methods described above regard measurements of stopped fission prod-ucts. Measurements of fission products without stopping them can be achievedas well. In these techniques, by measuring the kinetic energy and velocityof one fission fragment, the (E,υ) method, or of both fission fragments, the(2E,2υ) method, and based on the conservation of momentum in fission, themasses of the fission fragments are calculated. A low-energy and light particle-induced fission is one of the requirements of the method, so that the momen-tum of the inducing particle can be ignored. Another requirement is a thintarget, in order to minimise as much as possible the energy loss of the fissionfragments in the target. For the velocity measurement the time of flight tech-nique is applied, while for the energy measurement surface barrier detectorsmay be used.

Recoil spectrometers, such as Lohengrin at the Institut Laue-Langevin (ILL)in Grenoble [17], use the (E,υ) technique for studying unstopped fission frag-

14

ments. These spectrometers are coupled to the intense neutron flux of a reactor,and they achieve a mass separation by electromagnetic separation based on theenergy-charge state ratio (E/q). Specifically the spectrometer at ILL, performsan additional separation based on the mass-charge state ratio (A/q). Therefore,one of the disadvantages of this method is that in order for an independentyield distribution to be observed, the measurements have to be repeated forseveral kinetic energies and charge states.

Spectrometers, such as the Cosi-fan-tutte spectrometer at ILL, that makeuse on the (2E,2υ) technique, by measuring the time of flight and energyof each fission product, also exist, in this way avoiding the need of electro-magnets. More spectrometers have been constructed recently, like VERDI(VElocity foR Direct particle Identification) [18] constructed for the Joint Re-search Centre IRMM, Geel, Belgium, or are planned to be installed in the nearfuture, like the FALSTAFF (Four Arm cLover for the STudy of Actinide Fis-sion Fragments) spectrometer [19], to be installed in the Neutrons for Science(NFS) facility in SPIRAL2 [20], or the SPIDER spectrometer (SPectrometerfor Ion DEtermination in fission Research), located at the Los Alamos Na-tional Laboratory [21].

For identifying the nuclear charge the (∆E,E) technique is employed. Theenergy loss (dE/dx) of an ion passing through a material of known thickness,due to interactions of the ions with the shell electrons of the matter, depends onthe kinetic energy and charge Z of the ion. By measuring the energy loss ∆Eand the kinetic energy E, the nuclear charge Z of the nuclides can be deduced.

Another method for measuring fission yields, relatively recent, is based onthe inverse kinematics. The nuclide of interest is used as a projectile, acceler-ated to relativistic energies, and impinging on a stationary target. Because ofits interaction with the target, the projectile excites, resulting in fission. Thefission fragments are then separated in fragment separation, as in the case ofthe FRS (FRagment Separator) at GSI [22]. Studies of fission of almost anynuclide in the region above lead is possible with this method, which is one ofits strongest advantages.

The list of the different experimental techniques described in this section isfar from complete. New techniques with improved instruments are added tothe list all the time, aiming to a better understanding of the fission proocess.

The IGISOL techniqueA new method in order to improve the fission yield measurements in terms ofspeed and simplicity, has been developed at the University of Jyväskylä. Thismethod couples the chemical non-selectivity of the ion guide, in the sensethat ions of all chemical elements can be produced, with the superior massresolving power of the Penning Trap located at the University of Jyväskylä(JYFLTRAP), which allows identification of ions based only on their mass.Thus it is possible to measure isotopic yield distributions for a wide range offission products, based simply on their masses and by means of ion counting,

15

a clear distinction from the aforementioned techniques. It is worth mention-ing that a high precision in the nuclide mass determination is not considerednecessary, since these are used only for identification in the mass spectra.

The method cannot be used merely for deducing independent fission yieldsdistributions because of the chemical reactions introduced by the ion guideand the JYFLTRAP facility. However, if one independent yield of the isotopicyield distribution is known, the isotopic distribution can be directly convertedto the fission cross-sections for the other members of the isotopic chain. Thisis happening because the rate of production of a particular ion in the secondarybeam is directly proportional to its production cross section, since there is nosignificant accumulation and re-ionisation of the decay products, unlikely tothe classical ion sources [23], [24].

One of the advantages of this technique is that even nuclides with verylow yields can be detected thanks to the very low background. Hence, mea-surements of fission products can be performed, at the regions of the higheruncertainties, such as the tails or the valleys in the fission yield distribution ofn-induced fission on 235U [25]. On the other hand determination of more thanone fission observables is not possible with this technique, since the produc-tion of the fission fragments is integrated over several milliseconds before theyield is registered, and not on an event-by-event basis [26]. The experimentalsetup and procedure is described in detail in chapter 2.

16

2. Experimental Facility

2.1 The IGISOL technique combined with JYFLTRAPIn June 2010, the Ion Guide Isotope Separator On-Line (IGISOL) facility atthe Accelerator Laboratory of the University of Jyväskylä closed down for amajor upgrade, in order to be re-commissioned as IGISOL-4 in a new experi-mental hall. A new 30 MeV cyclotron (MCC30/15) was housed, which has thepossibility to accelerate protons (18 - 30 MeV) and deuterons (9 - 15 MeV),and is equipped with two beam lines thus offering access to a possible extrac-tion of two beams simultaneously. The maximum intensities that have beenmeasured inside the cyclotron are for protons 200 µA and 140 µA for 18 and30 MeV respectively, and for deuterons 62 µA for 15 MeV, exceeding designspecifications. However, it still has to be demonstrated what can be deliveredand indeed handled on target [27].

IGISOL has a long tradition of experiments on both neutron-rich fissionproducts and neutron-deficient nuclei, produced in light and heavy ion fu-sion reactions. Measurements of ground state properties, such as charge radiiand masses, and decay spectroscopy were covered in these experiments [28].In Fig. 2.1, a schematic overview of the facility is presented. The elements ofthe facility that are described in the text are denoted with numbers. In the caseof fission related experiments, the charged particle accelerated beam (protonsor deuterons), denoted with the red arrow in Fig. 2.1, impinges on a fissile tar-get which is placed inside the fission chamber in order for the fission reactionto occur. Neutron-induced fission is planned to be realised as well, where theaccelerated beam will bombard a Be target, placed in the reaction chamber, inorder to produce the neutron flux which will induce fission [29],[26]. The thintarget (14 mg/cm2 and 15 mg/cm2 for natTh and natU respectively) is one of thekey features of the IGISOL technique, as a significant fraction of the productshave enough recoil energy to pass the target and not stop within it. Heliumgas is flowing into the ion guide in order to slow down the fission products.In addition due to the high ionisation potential of the buffer gas the charge ofthe highly charged ions is reduced to the most probable +1 state. The He gasflow and the ion guide are denoted with the green arrow and 1 in Fig. 2.1respectively.

Afterwards, the ions are transported out of the ion guide with the help ofthe gas flow, and then accelerated with a voltage of 30 kV and guided to themass separator through a radio-frequency SextuPole Ion Guide (SPIG), indi-cated with 2 in Fig. 2.1, and electrostatic elements. The motivation for using

17

a multipole ion guide was to reduce the energy spread, and a higher ordermultipole than the common quadrupole is preferred as it can deliver highercurrent beam before becoming unstable (of the order of 1012 ions·s−1). Moreinformation about the SPIG can be found in [30] and the references therein.The differential pumping system is another key feature of the technique, as itallows efficient removal of the high gas load from the target chamber, whileat the same time keeping a sufficiently high vacuum along the beam line. Inthe dipole magnet, denoted with 3 in Fig. 2.1, the first mass selection ofthe produced fragments takes place based on their charge to mass ratio (q/m).The mass resolving power of the magnet is m/∆m ≈ 500. The desired beamis selected by slits located at the focal plane of the dipole and through theelectrostatic elements in the beam switchyard it is transferred either to the β -γ spectroscopy station or to the RadioFreQuency (RFQ) cooler and buncher,denoted with 7 and 4 in Fig. 2.1 respectively.

From the RFQ cooler and buncher, the isobarically purified beam can bedistributed either to the Penning Trap or the laser spectroscopy set up. In theRFQ, the preparation of the beam which will eventually enter into the PenningTrap starts. The continuous ion beam is accumulated over a period of time ofseveral ms, and cooled with the help of helium buffer gas. The cooled ionswill enter the Penning Trap in bunches with an energy spread reduced to a feweV so that a better precision can be realised in the measurement. In Fig. 2.1,the Penning Trap is denoted with 5 , while the laser spectroscopy beam lineis not shown since it was not used in the present work.

Inside the traps, a sequence of dipole and quadrupole excitations, as willbe explained in the next section, achieve a selection of the nuclides basedon their charge over mass ratio (q/m) with a resolving power up to ∼8·105,which is enough to resolve the elements of an isobaric chain, and sometimeseven isomeric states. After the extraction from the Penning Trap, the ions arecounted by a MultiChannel Plate (MCP) detector which is located at the endof the beam line, denoted with 6 in Fig. 2.1

2.2 Description of experimental elementsIn this section, the most important components along the beam line are pre-sented. More information can be found in a series of studies related to theIGISOL and JYFLTRAP facility ( [31], [32], [33], [34]).

2.2.1 The fission ion guideOne of the most important elements of the IGISOL method is the fission ionguide and the thin target which is placed within, as has been mentioned earlier.In Fig. 2.2 a schematic view of the fission ion guide, as seen from the top, ispresented. The cyclotron beam, olive green arrow in the figure, irradiates the

18

Fig. 2.1. Schematic overview of the IGISOL and JYFLTRAP facility, adapted from [26].

tilted fissile target, depicted in red colour. The thickness of the target is a cru-cial parameter for fission yield measurements, since a too thick target hindersthe products of escaping the target, while a too thin one allows the productsto leave the target with too high energy, thus decreasing the probability of thefragments to be stopped by the buffer gas. By placing the target in a tilted posi-tion, it is possible to use a thin target, while its effective thickness is increasedby a factor of almost ten.

One of the key features of the method is the He buffer gas, which flows intothe fission guide, aiming to slow down the products and cooling the target atthe same time. The energy of the highly charged fission products is decreaseddue to a sequence of collisions with the buffer gas atoms, while their chargestates are reduced via charge exchange reactions. Because of the high ionisa-tion potential of the buffer gas a considerable fraction of the ions end up at a+1 charge state. The fission products enter the stopping chamber, which is sep-arated from the small target volume by a thin Ni foil (0.9 mg/cm2) in order toprevent plasma effects caused by the primary beam. It is possible to use such awindow as the angular distribution of the fission fragments is almost isotropicand the stopping effect of the foil on the fission fragments is negligible. TheHe gas flow, typically at a pressure of 200 torr (∼ 267 mbar), guides the fissionproducts to the mass separator, through a 1.2 mm aperture in the exit nozzle,resulting in an evacuation time of a few tens of ms.

The design of the stopping chamber is an important parameter of the mea-surements since it can affect both the extraction time and the stopping effi-ciencies. Since the time needed to evacuate the gas chamber is typically ofthe order of a few tens milliseconds, it is evident that the design of the fissionguide generates a constrain in the ability of the method to measure properties

19

0 5 cm

Ni foil

He gas

Stopping chamber Target chamber

natU Target

Cyclotron beam

Fission products

Fig. 2.2. The IGISOL fission ion guide as it can be seen from the top, adapted from [24].

of short-lived nuclides. In fact of the whole experimental set up, the fissionguide is the slowest component until the RFQ cooler and buncher. The stop-ping efficiency defines the fraction of products which are stopped inside thebuffer gas. The produced fission fragments have a broad distribution of kineticenergies, so that the slowest ones cannot escape the target at all, while the oneswith the highest kinetic energy implant into the walls of the ion guide. Onlya fraction of the produced particles, those with the most appropriate energiescan be thermalised in the gas volume. Although mass dependence of the stop-ping efficiency in the ion guide is expected to exist, such an effect has notbeen observed experimentally since its first indication was mentioned in [33].Moreover, recent simulation studies on the stopping efficiency of the ion guideindicate that the systematic uncertainties due to the fission product mass andenergy are small with a proper selection of target thickness, and that a nickelfoil thickness of about 1 mg/cm2 results in a weak mass dependence in thestopping efficiency [24].

During the time the ions spend in the chamber, a limited number of chem-ical reactions can occur in the gas volume as deduced in [35], since the mostimportant ionisation mechanism is the nuclear reaction itself. Hence, the ionguide can be used for the production of almost any isotope, so in that sensethe technique is element independent. However, the efficiency of the ion guideis not expected to be the same for all elements, due to differences in the firstionisation potential, but the differences are expected to be small. As a proofof this, the deduced isobaric Z distributions from many works can be used([15], [33], [34], [36]). These distributions resemble a Gaussian distribution

20

as expected, something which would not be the case if the efficiency of the ionguide was strongly dependent on the chemical properties of the ions.

The total efficiency of the ion guide is the product of the stopping efficiencyand the extraction efficiency. All stopped ions can not be extracted from theion guide, due to interactions with walls, charge exchange reactions in thebuffer gas and radioactive decays that lead to ion losses. As a result, the ex-traction efficiency reduces the total efficiency of the gas cell, and it has beenmeasured at the upgraded IGISOL-4 to be 0.1% for 112Rh in proton-inducedfission. As a comparison, it is worth mentioning that at IGISOL-3 the sameefficiency was measured to be 0.02%.

2.2.2 Mass separatorAfter the ions are extracted from the fission guide, they are guided to the dipolemass separator. There, the first selection of the ion beam takes place basedon the charge over mass ratio (q/m). The desired ions are exiting the dipolemagnet through a fixed 7 mm slit, aligned vertically with respect to the focalplane of the magnet.

The trajectories of mass separated ion beams are handled with two electro-static beam benders, where the first one is a parallel plate beam kicker, used toblock the beam before the slit, so that the cooling cycle (tc) of the RFQ can becontrolled, as will be discussed in the next section. The second electrostaticbender at 30° is used to deflect the ions to the RFQ.

2.2.3 Radio-Frequency cooler and buncherThe capture of ions by the Penning Trap is more efficient if the separated ionshave low energy and if the beam is bunched instead of continuous. Therefore,the ions are first cooled and bunched by a so-called radio-frequency cooler andbuncher instrument (RFQ) [37].

The RFQ cooler and buncher is floating on a HV platform so that the ionsare decelerated from 30 keV to about 100 eV. Inside the RFQ, there is a highpurity (impurities of 10−5) helium gas at ∼10−2 mbar, in order to reduce thekinetic energy of the incoming ion beam, via collision with the atoms of thegas. The ions are accumulated inside the segmented linear radio-frequencyquadrupole field. They are confined axially due to a dc potential applied tothe segmented rods, while the applied quadrupole field creates the effectivepotential which guides the ions towards the symmetry axis of the RFQ. Thekinetic energy of the ions is decreased to the level of the helium gas due tocollision with it. Afterwards, the ions can be released in short bunches to thePenning Trap. A few ms are sufficient for the ions to cool down to eV levels,but the time spent by the ions in the RFQ (tc) is usually chosen to be equal

21

to the time the ions spend in the Penning Traps (tp), as will be explained insection 2.2.5.

2.2.4 Isobaric purification with JYFLTRAPThe JYFLTRAP facility consists of a double longitudinal Penning Trap andwas recently moved to the new location along with the IGISOL facility ([38],[39]). With the upgrade, new possibilities opened for the facility, such as sep-arate beam lines for JYFLTRAP and the collinear laser spectroscopy station,located after the radio-frequency quadrupole cooler and buncher.

In a Penning trap the ions are confined in two dimensions by applying astrong magnetic field (7 T in JYFLTRAP) parallel to the symmetry axis ofthe trap (~B = B~ez). By superimposing a static quadrupole potential in three ormore cylindrical electrodes, confinement in three dimensions can be achievedin a small volume of about 1 cm3.

The motion of an ion with mass m, charge q and velocity υ inside the trapis defined by the Lorenz force:

mr̈ = q(~E +~υ×~B) (2.1)

which leads to two radial oscillations at the angular frequencies ω+ and ω−and an axial motion at the angular frequency ωz:

ω± =12(ωc±

√ω2c −2ω2z ) (2.2)

ωz =√

qU0md2

(2.3)

where d is the characteristic trap dimension:

d =

√12(z20−

r202) (2.4)

and ωc is the rotational frequency of the charged particle in absence of electricfield:

ωc =qm

B (2.5)

The motion of the trapped ion can be represented by three eigenmotions towhich the aforementioned frequencies correspond. The ion trajectory is visu-alised in Fig. 2.3. Particularly, the slow radial oscillation, with the frequencyν− is called the magnetron motion and the motion with frequency ν+ is calledthe reduced cyclotron motion. The motion with frequency νz takes place alongthe axis of the magnetic field. The cyclotron frequency can be expressed as acombination of these three frequencies [40].

22

-1.5-1

-0.50

0.51

1.5

-1.5

-1

-0.5

0

0.5

1

1.5-2

-1.5

-1

-0.5

0

0.5

1

1.5

z

x

y

magnetron

reducedcyclotron

axial

Fig. 2.3. The ion’s trajectory in the Penning trap, figure adapted from [41].

ν2c = ν2++ν

2−+ν

2z (2.6)

The purification of the ion beam occurs in the first trap, the purificationtrap, which was the only one that was used in the fission yields experiments.In order for the ions to enter into the first trap, the axial potential wall at theinjection side is lowered below the kinetic energy of the ions. After the ionbunch arrives at the centre of the trap, the wall is restored, creating a potentialminimum at the centre of the trap along the axial direction. The purificationcycle of the bunch starts with cooling the ions through their collision with theHelium gas of 10−5 mbar with which the trap is filled. The amplitude of thefast motion (axial and the reduced cyclotron) is reduced, while the magnetronmotion amplitude slowly increases, as a result of the repulsive effect by theelectrostatic field. By applying a dipole excitation the magnetron radius of allions, independent of their m/q ratio is increased further. In order to preventthe loss of the ions due to their interactions with the electrodes of the trap,a quadrupole excitation at the cyclotron frequency νc is applied, so that themagnetron motion is converted to the reduced cyclotron motion, and the ions,whose mass and charge satisfy Eq. 2.5 are re-centered. The conversion ofmagnetron radius to cyclotron is illustrated in Fig. 2.4. Then the axial potentialwall on the extraction side is lowered, so that the ions are accelerated anddirected through a 1.5 mm aperture to the MCP detector at the end of the

23

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

x / mm

y / m

m

(a)

Fig. 2.4. The conversion of the magnetron motion to the cyclotron motion, figureadapted from [41].

beam line, after passing through the second trap (precision trap), which wasnot used in the fission yield experiments.

The whole procedure, as described above, typically lasts a few hundredmilliseconds, and is called the purification cycle, whose length is denoted astp. This time is closely related to the mass resolution that can be obtainedduring an experiment, since longer purification results in better resolution. Onthe other hand longer purification time may incur decay losses of short-livednuclei, so an optimisation of the cycle length should be achieved. The massdifferences for adjacent members of an isobaric chain increases the furtherfrom the line of stability they are, but they decrease closer to the valley ofstability or for isomeric states of the same isotope, so that a longer purificationcycle is necessary. Although decay losses are not an issue for the former case,where the isotopes are stable or long-lived, they might need to be taken intoaccount when isomeric states are measured. For the purposes of the currentstudies, the purification cycle was from 430 up to 660 ms.

The mass resolving power which can be achieved by the Penning Trap ism/∆m ≈ 8·105, much higher than the respective one of the magnet separator.As explained earlier, the mass resolution depends on the purification time, so itis clear that the width of the observed mass peaks depends on these settings andit is not an attribute of the masses themselves. A parameter in the purification

24

length that plays an important role is the cooling time. A longer one resultsin a better centring efficiency of the trapped ions of the desired masses, thusimproving the mass resolution and the transmission efficiency of the trap.

2.2.5 Timing Structure of the measurementFigure 2.5 illustrates the timing structure of the performed experiments. Themost time consuming part of the procedure is the purification cycle tc in thePenning Trap. By executing in parallel the preparation and the purificationcycle the time required for the experiments is reduced by half. As can been no-ticed in the figure, the preparation cycle (tb + tc) is set equal to the purificationcycle tp, so that a new bunch in the RFQ cooler and buncher is prepared, whilethe preceding one is purified in the trap. The space charge limit of the PenningTrap sets one more constrain to the size of the bunch, since this should not betoo big in order to avoid such effects. The amount of the ions inside the trapcould be reduced by simply lowering the cyclotron beam intensity, as in thiscase the yield of the long-lived species, which are produced at higher ratesand they actually cause the space charge effects, would be decreased. How-ever, this would keep the yield of the short-lived, less produced isotopes at anon-measurable level. Moreover, by adjusting the cooling cycle of the RFQ,the fraction of short-lived isotopes after the purification is enhanced, as in thisway the decay losses of short-lived isotopes in the RFQ are minimised. If thecooling cycle is set rather long, the decay-losses would be increased, whilethe long-lived species would keep on accumulating in the RFQ. Thus a shorttc and intense cyclotron beam is considered the optimal setting.

For each isobaric chain, a frequency scan was performed, which meansthat the cyclotron frequency νc was applied over the mass of interest. Theevents were detected by a MCP detector, located at the end of the beam line,after the Penning Trap, and the events were recorded together with the appliedfrequency scan, as will be explained in section 3. The frequency scan wasrepeated several times, in order to acquire adequate statistics, and the numberof these scans were varying in each case from 5 to 233.

25

Bunch # N-1

Bunch # N

Bunch # N+1

tp

RFQ

tc

TRAP

TRAP

tp

RFQ

ions purified in Penning Trap

TRAP

tp

RFQ

tc

TIME

ions collected to RFQ

ions blocked to enter RFQ

tb

tb tc

tb

total cycle time

Fig. 2.5. The selected purification cycle length tp dictates the timing of the experiment.While an ion bunch is purified in the Penning trap, the next bunch is prepared in theRFQ.

2.3 Chemical effects of IGISOL and JYFLTRAPEven though the IGISOL method is claimed to be chemically non-selective,this does not mean that it is completely free of chemical reactions. There arecertain places along the beam line, such as the fission guide and the PenningTrap, where chemical reactions may occur. Their occurrence and significancedepend on the number of impurities and on the time the ions spend in thesespecific environments. As explained in section 2.2.1, the evacuation time offragments is similar for all produced isotopes of an element and the impuritiesare at a constant, very low level. Nevertheless, since in the ion guide impuritylevels below sub-parts-per-billion are required, a completely new gas purifica-tion and gas transport system has been constructed at IGISOL-4, as describedin [27].

Another place which is filled with helium gas is the JYFLTRAP. Eventhough the gas pressure, and the impurities are much lower compared to theion guide, the ions spend about ten times longer time here than in the ionguide. Some reactive elements, like Zr and Y thus have sufficient time, toproduce molecules during the purification cycle. Charge exchange reactionsbetween the ion and the impurity atoms may occur as well. This concernsmainly elements with a high first ionisation potential, such as Kr and Xe, sothat weakly bound electrons of the impurity atoms may be captured by theions of these elements, resulting in their neutralisation. As can easily be un-derstood, the buffer gas is the main source of impurities in the system, while itis also very essential for the operation of the RFQ and JYFLTRAP. Although

26

chemical reactions can not be fully avoided, one way to overcome this issue,is to perform relative measurements instead of determining absolute yields.

27

3. Data Analysis

The data of this work were acquired with two different methods. The IGISOLtechnique was employed in all experimental campaigns, while in June 2013the yields of the products were also measured by means of γ-spectroscopy. Inthis section the analysis which was developed and followed in order to deducethe isomeric yield ratios from both methods is presented.

3.1 Penning Trap DataThe obtained data is a result of several experimental campaigns, that took placefrom April 2010 until May 2014. The first performed measurement was con-cerning the proton induced fission of Thorium, and it took place at IGISOL-3.Since then the facility was upgraded to IGISOL-4, as described in chapter 2,and the rest of the experiments were performed in the completely renewedfacility. In the following table the date of the performed experiments are sum-marised together with the status of the facility at that time.

Experimental Runs

p - Th April 2010 IGISOL-3April 2014 IGISOL-4

p - UJune 2013 IGISOL-4

August 2013 IGISOL-4May 2014 IGISOL-4

Table 3.1. Kind and date of the experiments performed for this work.

The analysis of the data acquired from JYFLTRAP (mass purified data) isa multistep procedure, consisting of processes such as the spectra generation,the selection of desired events based on their time of flight, the analysis of thechosen ones by the counts-in-peak method and finally the corrections of thecalculated yield due to radioactive decay. These steps are described in detailin the following sections.

Each saved data file contains information about the time and the settingsof the experimental run. Specifically, in the recorded file there is informationregarding the scanning frequency, the Time of Flight (TOF) and number ofcounts for every detected ion.

29

3.1.1 Time of flight selectionThe ions leave the purification trap with the same energy, so their Time OfFlight (TOF) depends only on the mass. This results in one peak in the TOFdistribution, which can be distinguished easily, and by gating on this peak aselection only of the desired events can be achieved so that only these will beused for the later analysis. In this way, random noise that is registered in theMCP detector, and appear in the time of flight spectrum as small peaks or asrandomly distributed events, can be eliminated. These events are generated ei-ther by false triggers of the detector or by discharging sparks of real ions fromJYFLTRAP. However they can be treated as background noise since they donot belong to the elements that are aimed to be measured. A TOF distributionspectrum is depicted in Fig. 3.1, where the coloured peak, which correspondsto the TOF of the masses of interest, is clearly seen. The vertical lines oneach side of the peak defines the gate on the distribution, so that only eventswithin this specific time of flight range will be analysed. By gating on the TOFdistribution a background subtraction can be achieved, which in most cases issufficient and no further background reduction is needed.

s)µTime Of Flight (0 100 200 300 400 500

Cou

nts

1

10

210

310

Time Of Flight

Fig. 3.1. Time of Flight distribution of mass A=96. The red lines depicts the eventsthat were selected to be further analysed.

In Fig. 3.2, the contribution of the TOF gating on the background subtrac-tion can be noticed. In (a), the raw frequency spectrum is presented, beforeany TOF gating and thus background subtraction, while in (b), the same mass

30

spectrum after gating on the most prominent peak on the TOF distributionspectrum is depicted.

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4310×

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 310×

020406080

100120140

Frequency [kHz]

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4310×

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 310×

Cou

nts

020406080

100120140

1120.3 1120.32 1120.34 1120.36 1120.38 1120.4310×

1120.3 1120.32 1120.34 1120.36 1120.38 1120.4 310×

0

2

4

6

8

10

12

(a)

(b)

(c)

Sr mY Y

Fig. 3.2. The effect of the TOF gating on the background subtraction on a frequencyspectrum is visualised. In (a), the black histogram represents the frequency spectrumof mass A=96 without any background subtraction, while the red histogram shows theevents after the TOF gating. In (b) the same mass spectrum, but only after the TOFgating is shown and in (c) the background events are depicted.

3.1.2 Peak intensity determinationIn order to calculate the isomeric yield ratios, the intensity of the peaks inthe frequency spectrum had to be deduced and then compared to each other.For the identification of the masses appearing in the spectrum, a cyclotronfrequency calibration based on the evaluated atomic masses was used [42].

The height of the mass peak can be considered as a direct measurement ofthe beam intensity since the maximum transmission efficiency is achieved atthe cyclotron frequency. By fitting a gaussian function to these peaks, theirheight can be calculated. In the Penning trap spectrometer, the shape of themass peak is not uniform for all cases, but it strongly depends on the settingsof the trap. However, in our case, the approach of a gaussian function withcertain constraints can be considered adequate, especially since a number ofcriteria are fulfilled. The shape and the width of the peaks are believed to beinvariant for given settings, so that the peak area and height can both equallyrepresent the beam intensity. Therefore the number of counts is possible to

31

be used for the extraction of the yield ratio, since both the nominator and thedenominator in the fraction are estimated from the same experiment.

In the present work, all the fits were performed by applying gaussian func-tions on the experimental peaks. Specifically, a function consisting of the samenumber of gaussian functions as the number of the peaks in the spectrum wascreated. One condition for this function was the width of the peaks to be thesame for all masses, since this represents the detection resolution, which is re-lated to the applied quadrupole excitation of the Penning Trap, as has alreadybeen explained in subsection 2.2.4. For example, in a case with three peaks wecreate a function which consists of three gaussian curves as shown in Eq. 3.1.

G1(x) = A1 · exp(−(x− xre f )2

2σ2)+A2 · exp(−

(x− xisom)2

2σ2)

+A3 · exp(−(x− xgs)2

2σ2)

(3.1)

where A1, A2 and A3 stand for the height of each peak.A problem that arises from the analysis is where to define the peak positions,

especially since we are interested in isomeric states, which most of the timesare lying very close to the ground state, and thus they overlap. For the exactposition of the peaks, which are depicted as xre f , xisom and xgs in the aboveequation, we take advantage of the fact that in the measured spectra there isat least one isolated and well defined peak, which corresponds to a knownmass. This mass is usually the precursor (or the daughter) of the nuclide ofinterest, before (or after) its β -decay. This peak is taken as the xre f and sincethe masses are adequately known, at least enough for our purpose, in order todefine the position of the isomeric state we are making use of the followingequation:

xisom×misom = xre f ×mre f (3.2)

and by solving it for xisom, we have that

xisom =mre fmisom

× xre f (3.3)

It is evident that the position of the peaks in the spectrum are defined relativeto their standard distance from the isolated peak, reducing this way the numberof the unknown parameters in Eq. 3.1 to five, and resulting in:

G(x) = A1 · exp(−(x− xre f )2

2σ2)+A2 · exp(−

(x− misommre f · xre f )2

2σ2)

+A3 · exp(−(x− mgsmre f · xre f )

2

2σ2)

(3.4)

32

In cases where more than three peaks were present in the spectrum, a proce-dure similar to the one described above was followed, with the only differencethat the G1(x) consisted of more than three gaussian functions. In all cases thereference point was taken from the best defined peak in the spectrum.

The intensity of each peak was calculated afterwards by integrating a gaus-sian function on each peak. For the values of the parameters of the new definedgaussian, the values of the fitted peaks were used, managing this way each ofthe peak to have the same width. It is not necessary that the peak width hasthe same value for the measurements of all experiments, as has been alreadydescribed, since the achieved resolution strongly depends on the settings ofthe Penning Trap. It is sufficient as far as it stays constant for the same mea-surement, and as quality assurance it is desired that the σ of the gaussian to besimilar for similar settings of the trap.

In Fig. 3.3 an example of a frequency distribution is illustrated after theTOF gating. The red dashed line represents the gaussian fitted function G(x),which in this specific case consists of three gaussians.

Frequency [kHz]1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4

310×

Cou

nts

0

20

40

60

80

100

120

140

A=96

Sr mY Y

Fig. 3.3. Frequency distribution spectrum of mass A=96. The peak positions of96mY and 96Y are calculated relative to 96Sr, which is taken as reference. The peakidentification is based on a frequency to mass calibration. The red dashed line showsthe gaussian fitted function G(x).

33

3.1.3 Corrections due to radioactivityThe ions travel the distance from their creation in the IGISOL chamber totheir detection in the JYFLTRAP, typically in some hundreds of ms, so duringthis travel path some losses due to radioactive decays will occur. The ionsspend about 90% of this time mainly in the RFQ and the traps, so radioactivedecays are most likely to happen there. There are three potential ways in whichradioactive decays can affect a measurement:

• β -decay daughters can be released from the surfaces of the IGISOLfront-end (i.e the walls of the ion guide and the surfaces of the SPIGelectrodes.).

• β -decay products can be captured in the trap.• decay losses because of the radioactive decays from short-lived nuclides.

Due to the nature of the fission reaction and the settings of the traps, thecontribution of the first two factors, for different reasons in each case, is notvery significant, as it has been investigated and described in detail in pre-vious works [31], [43]. Specifically the overall transmission efficiency ofJYFLTRAP is∼0.01%, so a lot of ions are either lost in the ion guide or are ex-tracted as neutral or multiple charged ions. It has been studied thoroughly, thateven in the worst case the contribution to the yield of the isotope of interestdue to the release of β -decay products does not exceed 1%.

The contribution of the β -decay that can be captured in the trap and thus dis-turb the observed yield of the nuclide of interest is expected to be small, if notnegligible. This happens because of the nature of fission, and due to the veryshort time of the purification cycle, which is usually of the order of ms. Hence,only very exotic isotopes can decay during these times, but their fission crosssections decrease rapidly towards the very exotic area of the neutron rich iso-topes, approximately about a factor of ten per mass unit. Since this productionratio is very small, it is expected that even if all decay products were trapped,this would increase the measured yield of about 10%. The decays of the mostproduced to the less abundant and stable isotopes can be ignored, since this isunlikely to happen due to their long half-lives. Since fission produces isotopeson the neutron rich side of the chart of nuclide, a possible β -decay will resultin a doubly charged ion, because of the change of the nuclear charge. The Pen-ning Trap is tuned though for single charged particles, so even if the β -decayproducts will be trapped, they will be eliminated in the purification cycle.

Decay losses due to radioactive decaysAs already mentioned, the ions spend most of their time from their creationto their detection in the MCP, in the RFQ and the Penning Trap, so this is theonly time that needs to be taken into account in order to apply corrections forlosses due to radioactive decays within these two apparatuses. The evacuationtime from the ion guide is rather short and it can be neglected for these correc-tions. Thus, the correction function consists of two components, one for the

34

radioactive decays that occur during the preparation cycle tc of the RFQ, andthe other due to the decays during the purification cycle tp of the Penning Trap.In the current experiments these two times were equal, but they were varyingfrom 430 up to 660 ms depending on the experiment. Short-lived nuclides willdecay during this time interval, so corrections due to the decays are consideredto be important especially for the most short-lived ones. The detected numberof ions N of a certain nuclide is taken to be proportional to the initial numberof ions N0, that are extracted from the ion guide, in case the transmission andthe detection efficiency are excluded. Then the ions are assumed to enter theRFQ at a constant rate N0/tc, which is equal to a typical radioactive growth-inperiod, expressed by the first term in Eq. 3.5. Afterwards, a bunch of ions areejected from the cooler and enter in the trap, and only ions that decay in thetraps during the purification cycle tp are lost. These losses are expressed by thesecond term of Eq. 3.5. The equation that can be applied for these correctionsis:

N =N0tcλ· (1− e−λ tc) · e−λ tp (3.5)

where λ is the decay constant of the nuclide. A part of the above equation canbe taken as the correction function ψ , which depends on the decay constant λ :

ψ(λ ) = tcλ ·eλ tp

1− e−λ tc(3.6)

so that the relation between N and N0 can be expressed as:

N0N

= ψ(λ ) (3.7)

The uncertainty of the corrected mass peak intensity is given by:

∆N0N0

=

√(∆NN

)2+

(∆ψ(λ )ψ(λ )

)2(3.8)

where the first factor represents the statistical uncertainty of the peak intensity,and the second one the uncertainty of the correction function ψ , which is afunction of the half-life of the measured isotope. The statistical uncertainty∆N can be calculated from the experimental data. The uncertainty of ∆ψ canbe estimated from the uncertainty of the decay constant λ of the nuclide ofinterest and the derivative of ψ:

∆ψ(λ ) = ∆λ ·ψ ′(λ ) (3.9)

where, the uncertainty of λ is calculated from the half-lives taken from theNubase2012 evaluation of nuclear properties tables [42], and the derivative ofψ is:

ψ ′ =tcλ

e−(tc+tp)λ −(

tp +1λ

)(3.10)

35

In the present study, the decay corrections were applied whenever the half-lives of the nuclides were smaller than ten times the purification cycle length tp.The decay correction function ψ(λ ) decreases monotonically with half-life,where longer half-lives correspond to smaller correction and shorter half-livesto bigger ones. It is thus easier, instead of computing the uncertainty of thecorrections function with algorithms, to deduce this uncertainty by the upperand lower limits [43]. This uncertainty is expected to be asymmetric and morepronounced for the short-lived nuclides, because of the non-linearity of the cor-rection function ψ(λ ). A symmetric approximation of the uncertainties wereconsidered to be sufficient though for the present work, since the half-livesof the detected nuclides were, in the worst case comparable to the sum of thecooling and purification time. Therefore the correction function’s uncertaintyis calculated by symmetric intervals of the average value of ψ(λ ), as follow:

∆ψ(λ )avg = (ψ(λ +∆λ )+ψ(λ −∆λ ))/2 (3.11)

For the calculation of ψ(λ +∆λ ) and ψ(λ −∆λ ) in the above equation λ wassubstituted with (λ +∆λ ) and (λ −∆λ ) respectively in Eq. 3.6.

3.2 γ-spectroscopy DataIn parallel with the Penning trap measurements in June 2013, γ-spectroscopydata for the same isobaric chains were taken as well by using a HPGe detec-tor, so that the results from the two different experimental techniques can becompared to each other, and thus the consistency of the upgraded facility eval-uated. The secondary produced beam is separated with a 55° dipole magnetresulting in the selection of an isobaric chain with the desired mass numberA. As already mentioned a mass separation at the order of m/∆m = 500 canbe achieved from the magnetic dipole magnet. After the separation, the elec-trostatic switchyard is turned to a dedicated γ-spectroscopy setup, so that thebeam instead of proceeding to the RFQ cooler and the JYFLTRAP, will betransported to the spectroscopic station. The ions are implanted in an alu-minium foil, placed in front of the detector, so that γ-ray data can be collectedon-line for several hours. This technique can be applied to all short-lived fis-sion products with know γ-ray intensity and decay constants. The constraintsof this method regard the cases where the products are stable, or they decaywithout γ-ray emission, or their intensities or half-lives are not well known.

For the analysis of the acquired spectra the code TV, developed at theUniversity of Cologne (Germany), was used ([44]). The intensity of the de-sired peaks was calculated by performing a gaussian fit. In each case andbefore every measurement, the background activity was recorded and after-wards subtracted from the spectrum of interest. By doing this, the reductionof the buildup of long-lived activities along the beam line ("instrumental back-ground") could be achieved. The γ-rays that were used for the determination

36

of the isomeric yield ratios are presented in Tab. 3.2, together with their decayprobabilities and their half-lives. In the table, only the most intense γ-ray ofeach nuclide is written. If more than one γ-ray could be determined quanti-tatively, the yield is calculated from the weighted average of all consideredγ-rays.

Mass Nuclide Eγ (keV) Iγ (%) T1/2 (sec) Nuclear Library

81 31Ga 216.8 37.4 1.22 [45]m32Ge 2174.3 6.3 7.6 [45]32Ge 1495.5 19.9 7.6 [46]

97 38Sr 1905.0 25 0.43 [45]m39Y 161.4 72.5 1.17 [46]39Y 3287.6 18.1 3.75 [46]

m41Nb 743.5 100 58.7 [46]41Nb 657.9 98.2 4326 [46]

128 49In 2104.1 6.5 0.845 [46]m50Sr 831.5 100 6.5 [46]50Sr 482.3 59 4744 [46]

130 m50Sr 144.9 23 102 [46]50Sr 780.4 56.4 223.2 [46]

Table 3.2. Nuclear data used for the analysis and the deduced isomeric yield ratios.Only a main characteristic γ-ray of each nuclide is listed.

The determined intensity (Y measγ (A,Z))) of each peak, had to be correctedfor its intensity (Iγ ) and for the efficiency (ε(Eγ )) of the HPGe detector for thisspecific energy.