Neutrino-nucleus :Measurements vs. calculations

Petr Vogel, Caltech

Oak Ridge, Aug. 28-29, 2003

Outline: a) review of known weak processes b) successes and difficulties c) unknown but important processes d) why we need to `calibrate’ nuclear structure models

Note for the web etc. version:

Throughout the selection of references is

rather subjective and incomplete.

Also, to save space, usually only the first author

and year are given. Aficionados will easily

recognize the correct reference.

• The simplest system – a single nucleon

These two processes are governed by the same

hadronic matrix element:

n p + e- + e (neutron decay)

e + p n + e+ (inverse neutron decay)

Knowing the neutron lifetime, 885.7(0.8), fixes the

cross section for the relevant energies.

The (relatively) small corrections of order E/Mp and

can be accurately evaluated.

(see Vogel & Beacom, Phys. Rev. D60,053003 (1999) and

Kurylov, Ramsey-Musolf & Vogel, Phys.Rev.C67,035502(2003))

In this way the cross section of the inverse neutron decay can

be evaluated with the accuracy of ~0.2%.

A more complicated system – the deuteronThere are many possible reactions now:

e+ d p + p + e- (CC)

d n + p + (NC)

the corresponding reactions with antineutrinos as well as

p + p d + e + e+ (pp in the Sun)

p + p + e- d + e (pep in the Sun)

For all these reactions all unknown effects can be lumped

together in one unknown parameter L1A (isovector two-body

axial current) that must be fixed experimentally

(calibrating the Sun).

The cross section is of the form

(E) = a(E) + b(E)L1A, where the functions a(E), b(E) are

known, and b(E)L1A contributes ~`a few’ % .

Fixing the parameter L1A

There are several ways to do this. One can use reactor

data (eCC and NC), solar luminosity + helioseismology,

SNO data, and tritum beta decay. Here is what you get:

reactors: 3.6(5.5) fm3 (Butler,Chen,Vogel)

Helioseismology: 4.8(6.7) fm3 (Brown,Butler,Guenther)

SNO: 4.0(6.3) fm3 (Chen,Heeger,Robertson)

tritium decay: 6.5(2.4) fm3 (Schiavilla et al.)

All these values are consistent, but have rather large

uncertainties. To reduce them substantially, one would

have to measure one of these cross sections to ~1%.

This is very difficult.

Reaction e12C 12Ng.s.+ e-

This is an example of a process where the cross

section can be evaluated with little uncertainty.

We can use the known 12N and 12B decay rate,

as well as the exclusive capture on 12B and

the M1 formfactor for the excitation of the

analog 1+, T=1 state at 15.11 MeV in 12C.

This fixes the cross section value for (almost)

all energies, for both e and .

A=12 triad

QMeV

Q= 13.37 MeV

Experiment and theory agree very well(this reaction can be used for calibration)

Exp.results (in 10-42cm2):

9.4 0.4 0.8 (KARMEN e, 98, DAR)

8.9 0.3 0.9 (LSND e, 01, DAR)

56 8 10 (LSND , 02, DIF)10.8 0.9 0.8 (KARMEN, NC, DAR )

Calculations: 9.3 , 63, 10.5 (CRPA 96) 8.8 , 60.4, 9.8 (shell model, 78) 9.2 , 62.9, 9.9 (EPT , 88)

Cross section for 12C(12Ngs in 10-42cm2,see Engel et al, Phys. Rev. C54, 2740 (1996)

e + 12C 12N* + e- (inclusive reaction)

Here the final state is not fixed and not known,

one cannot use (at least not simply as before)

the known weak processes to fix the parameters

of the nuclear models.

The measurement is also more difficult since the

experimental signature is less specific

(units as before 10-42cm2):

4.3 0.4 0.6 (LSND, 01)

5.7 0.6 0.6 (LSND, 97)

5.1 0.6 0.5 (KARMEN, 98)

3.6 2.0 (E225, 92)

Evaluation of the for inclusive12Ce,e-)N* with DAR spectrum

This is dominated by negative parity multipoles,

calculation becomes more difficult. Here is what

various people get (in 10-42cm2):Kolbe 95 5.9-6.3 CRPA

Singh 98 6.5 local density app.

Kolbe 99 5.4-5.6 CRPA, frac. filling

Hayes 00 3.8-4.1 SM, 3hextrapolated

Volpe 00 8.3 SM, 3hVolpe 00 9.1 QRPA

The agreement between different calculations, and with the

experiment, is less than perfect.

True challenge, inclusive12C()N* with DIF

Exp: LSND 02, (10.6 0.3 1.8)x10-40cm2

Calc: 17.5 – 17.8 (Kolbe, CRPA, 99)

16.6 1.4 (Singh, loc.den.app.,98)

15.2 (Volpe, SM, 00)

20.3 (Volpe, QRPA, 00)

13.8 (Hayes, SM, 00)

Thus all calculations overestimate the cros section, with SM results noticeably smaller than CRPA or QRPA. The reason for that remains a mystery.

But CRPA describes quite well electronscattering with similar momentum transfer

Moreover, in another case (and a bit lower energies) CRPA (Kolbe) and SM (Haxton 87)

agree quite well.

CRPA angular distribution (which at low energy also agrees with SM)

Let me now show some calculated forseveral cases of practical interest (ICARUS).These could be, therefore, used as both tests

of calculations and basis for detector design etc.

40Ar(e,e-)40K*, and40Ar(e,e+)40Cl* RPA

CC cross section for e (T=4 MeV) on 52-60Fetotal (full circles), n emission (empty), p (crosses)

Reaction e,e-)127Xebound states

This was proposed by Haxton,88 as a radiochemical

solar detection reaction, similar to 37Cl. The cross

section, unlike 37Cl, was based only on difficult calculations.

To calibrate it, an experiment with DAR

spectrum was performed at LAMPF, giving stat)(syst))x10-40cm2 (Distel 02)

Calculations, performed earlier (Engel 94) gave 2.1 (for gA=1.0) or 3.1 (for gA=1.26)

The agreement is good, but the experimental uncertainty

is large, and the issue of gA renormalization remains

unresolved.

Charged current cross section on Pb

Lead based detectors are considered for SN detection.

There are no experimental data, so the detector design

has to rely on calculated cross sections.

Shell model treatment is impossible for such heavy nucleus,

so various forms of RPA and other approximations are used.

The spread of the calculated values is often treated (for no

logical reason, but nevertheless) as a measure of uncertainty

of the calculated values.

Calculated CC cross sections fore on 208Pb (in 10-40 cm2)

For DAR: Kolbe & Langanke, 01 36 Suzuki & Sagawa, 03 32For FD: T=6 MeV 8 MeV 10 MeV 14 25 35 Volpe 02 11 25 45 Kolbe 01 Considerably larger were obtained by Fuller et al. 99;reasons for that overestimate are well understood, seeEngel et al. 03 where the are close to Volpe 02

CC on 208Pb calculated with SKIII (solid) and SkO+ (dashed) interactions, in fm2. From Engel et al. 03

Conclusions:

1) Comparison between calculated and measured cross sections on complex

nuclei is sporadic or nonexistent. Reliable and accurate data are needed2) Different calculations agree on a ~30% level for the energies relevant to SNS or Supernovae. 3) However, if some (even small) number of parameters could be adjusted (as for the

12C 12Ng.s.) a much better description will likely result.

Here are few slides I showed at the

ORLAND workshop three years ago.

They remain basically relevant for SNS2.

(or SNS2)

(or SNS2)

(or SNS2)

(or SNS2)

(the smaller is rate is more correct)