TEMPERATURE AND DENSITY OF HOT

DECAYING 40CA AND 28SI

Katarzyna Schmidt

University of Silesia, Katowice, Poland

K. Schmidt, J. B. Natowitz, M. Barbui, K. Hagel, A. Bonasera, G. Giuliani,H. Zheng, M. Rodrigues, R. Wada, M. Huang, C. Botosso, S. Kowalski

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INTRODUCTION

During the last decade it was theoretically shown that dilute sym-metric nuclear matter may experience Bose particle conden-sation. This possible new phase of nuclear matter may have itsanalog in low-density states of α-conjugate lighter nuclei.

Theoretical calculations show that self-conjugate N = Z nucleiwill cluster into a metastable phase of α particles at excitationsabove 3MeV/nucleon and densities below 0.33 normal density

The preliminary results of temperature and density of hot decay-ing 40Ca and 28Si will be presented. The method used allows totrace important quantum effects such as fermion quenching orBose - Einstein Condensation in nuclei.

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EVENT SELECTION - WHAT WE NEED

careful isolation of the equilibrated sourceelimination of particles emitted before equilibriumevents with fragments that have an α-like (i.e. 12C, 16O, etc.)or d-like structure (6Li, 10B, etc.).

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EVENT SELECTION - WHAT WE HAVE

Investigation of 40Ca + 40Ca at 35 MeV/A:

subject: peripheral and midperipheral collisions leading toexcited projectile-like fragmentstotal equilibration of all degrees of freedom is not achie-ved in the midperipheral collisionsZ = 1 particles and neutrons are primarily pre-equilibriumparticles, representing energy dissipation but not energydeposition into the PLFa hierarchy effect is observed in the collision dynamicsmechanism significantly increases the difficulty of isolatingclean projectile decay samples

Phys. Rev. C(95) 054618 (2017)

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EVENT SELECTION

1 ATOT = 40 + ALCP :even - even fragmentsodd - odd fragmentseven - odd fragmentsmixed fragmentsbosonic fragmentsfermionic fragments

2 α-like mass = 40 and α-like fragments3 α-like mass = 40 and 10 α4 d-like mass = 40 and d-like fragments

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EXCITATION ENERGY CALCULATIONS

Total excitation energy:

E∗TOT =∑

i

K i − Q

Transverse excitation energy (to minimise contributions fromentrance-channel effects, predominant in the beam direc-tion):

E∗TH =32

∑i

K i⊥ − Q

For a completely equilibrated system, the transverse kineticenergy (times 3/2) is equal to the total kinetic energy.

equilibrium observable: E∗R =E∗TOTE∗TH

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EVENT SELECTION - EQUILIBRIUM TEST

E∗R on Z-axis

0.0 0.4 0.80.0

0.1

0.2

0.3

0.4

0.5

0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.80.00

0.25

0.50

0.75

1.25

1.50

1.75

2.00

Sphericity

Copla

nari

ty

Mixed Even-Even Bosonic -like

0.8 < E∗R < 1.2

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EVENT SELECTION - STATISTICS

100 101 102 103 104 105

Number of Events

Mixed

Even-Even

Bosonic

-like

Odd-Odd

Even-Odd

Fermionic

10

deuterium-like

130435

73726

80517

69153

439

156

156

344

205

No Cut

100 101 102 103 104 105

Number of Events

Mixed

Even-Even

Bosonic

-like

Odd-Odd

Even-Odd

Fermionic

10

deuterium-like

78130

41996

46235

39526

226

88

88

262

117

After E*R Cut

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THE METHOD - CLASSICAL AND QUANTUM CASE

classical case:σ2

xy = N̄4m2T2

quantum case:σ2

xy = N̄4m2T2QF

QF - quantum factor, different for bosons and fermions

For bosons, the below and above T0 case has to be consi-dered. In this presentation - the below T0 case will be shown.

Physics Letters B 696 (2011) 178–181Nuclear Physics A 892 (2012) 43–57Nuclear Science and Techniques 24 (2013) 050512Phys Rev C 86 (2012) 027602

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THE METHOD - COULOMB CORRECTIONS

〈Q2xy〉 = (2mT )2 4

15

∫∞0 dyy

52 1

ey+ A′

yVT2 −ν±1∫∞

0 dyy12 1

ey+ A′

yVT2 −ν±1

〈 (∆N)2

N̄〉 =

∫∞0 dyy

12 e

y+ A′yVT2 −ν

ey+ A′

yVT2 −ν±1∫∞

0 dyy12 1

ey+ A′

yVT2 −ν±1

N̄ =gVh3 4π

(2mT )3/2

2

∫ ∞0

dyy12

1

ey+ A′

yVT2−ν ± 1

V, T, ν are the roots of the equations, A′ = 1.444π~2ZparticleZsource

2m

ρ =gh3 4π

(2mT )3/2

2

∫ ∞0

dyy12

1

ey+ A′

yVT2−ν ± 1

Phys Rev C 88 (2013) 024607, H. Zheng PhD thesis 10 / 17

AVERAGE MULTIPLICITY N̄

50 150 250 3500

1

2

3

4

5

6

7

50 150 250 350 50 150 250 350 50 150 250 350

40Cap

d

t

6Li7Li

E*[MeV]

N

-like Bosonic Even-Even Mixed

50 150 250 3500

1

2

3

4

5

6

7

50 150 250 350 50 150 250 350 50 150 250 350

28Sip

d

t

6Li7Li

E*[MeV]

N

-like Bosonic Even-Even Mixed

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MULTIPLICITY FLUCTUATIONS MF

50 150 250 3500.0

0.5

1.0

1.5

2.0

50 150 250 350 50 150 250 350 50 150 250 350

40Cap

d

t6Li7Li

E*[MeV]

MF

-like Bosonic Even-Even Mixed

50 150 250 3500.0

0.5

1.0

1.5

2.0

50 150 250 350 50 150 250 350 50 150 250 350

28Sip

d

t6Li7Li

E*[MeV]

MF

-like Bosonic Even-Even Mixed

XG. Cao et al., Evidence for high excitation energy resonances in the 7 alpha disassembly of 28Si,

https://arxiv.org/abs/1801.07366

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QUADRUPOLE FLUCTUATIONS QF

50 150 250 350107

108

109

1010

50 150 250 350 50 150 250 350 50 150 250 350

40Cap

d

t

6Li7Li

E*[MeV]

QF

-like Bosonic Even-Even Mixed

50 150 250 350107

108

109

1010

50 150 250 350 50 150 250 350 50 150 250 350

28Sip

d

t

6Li7Li

E*[MeV]

QF

-like Bosonic Even-Even Mixed

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TEMPERATURE DISTRIBUTION

50 150 250 3500

2

4

6

8

10

12

14

50 150 250 350 50 150 250 350 50 150 250 350

40CaTcl

Tq

Tcoul

E* [MeV]

Mixed MatterT [

MeV

]6Li d p

50 150 250 3500

2

4

6

8

10

12

14

50 150 250 350 50 150 250 350 50 150 250 350

28SiTcl

Tq

Tcoul

E* [MeV]

Mixed Matter

T [

MeV

]

6Li d p

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DENSITY DISTRIBUTION

0 1 2 3 4 5 6 7

10-5

10-4

10-3

10-2

10-1

100

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

40Ca0.33

p

d

t

6Li

T[MeV]

/0

-like Bosonic Even-Even Mixed

0 1 2 3 4 5 6 7

10-5

10-4

10-3

10-2

10-1

100

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

28Si0.33

p

d

t

6Li

T[MeV]

/0

-like Bosonic Even-Even Mixed

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SUMMARY

density and temperature of hot decaying PLFshave been extractedwe obtained similar results, regardless the event selectionwe observe different temperatures of the PLF at the emis-sion of each particle and therefore different time scales ofthe different particle-types emission.bosons experience higher densities than tritons; protons seemto be emitted from the same region of the nuclei as bo-sonsthe comparison with the theoretical calculations will be per-formedthe above T0 case for bosons will be performedthe calculations of T and ρ of decaying 28Si for other typeof matter is ongoing.the hypothesis the THSI are the BEC needs to be confirmed

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BACKUP

100

101

102

103

104

105

106

E* = 0

mean = 0.0658

rms = 0.2640

MF = 1.0583

E* = 20

mean = 0.0271

rms = 0.1688

MF = 1.0498

E* = 40

mean = 0.0500

rms = 0.2258

MF = 1.0189

E* = 60

mean = 0.0802

rms = 0.2874

MF = 1.0303

100

101

102

103

104

105

106

E* = 80

mean = 0.1140

rms = 0.3443

MF = 1.0398

E* = 100

mean = 0.1487

rms = 0.3889

MF = 1.0172

E* = 120

mean = 0.1705

rms = 0.4140

MF = 1.0049

E* = 140

mean = 0.1937

rms = 0.4411

MF = 1.0045

100

101

102

103

104

105

106

E* = 160

mean = 0.2147

rms = 0.4647

MF = 1.0061

E* = 180

mean = 0.2229

rms = 0.4816

MF = 1.0404

E* = 200

mean = 0.2027

rms = 0.4391

MF = 0.9511

E* = 220

mean = 0.2265

rms = 0.4935

MF = 1.0754

0 5 10 15

100

101

102

103

104

105

106

E* = 240

mean = 0.3056

rms = 0.6866

MF = 1.5429

0 5 10 15

E* = 260

mean = 0.3415

rms = 0.4742

MF = 0.6585

0 5 10 15

E* = 280

mean = 0.0667

rms = 0.2494

MF = 0.9333

0 5 10 15

E* = 300

mean = 0.1111

rms = 0.3143

MF = 0.8889

Multiplicity

Even-Even, A = 3

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