GDR Studies at VECC Facility Sudhee R. Banerjee Variable Energy - - PowerPoint PPT Presentation

Variable Energy Cyclotron Centre, Kolkata, India

GDR Studies at VECC Facility

Sudhee R. Banerjee

Outline

Introduction A few measurements at VECC K-130 Cyclotron

with LAMBDA photon spectrometer

• Jacobi shape transition
• Super-deformation in 32S – orbiting or clustering?
• Coherent bremsstrahlung in 252Cf spontaneous fission
• Evolution of GDR widths with Temperature
• GDR strengths in 252Cf fission fragments
• GDR widths at very low temperatures
• Isospin symmetry breaking/restoration in excited nuclei

Plans for the VECC Super-conducting cyclotron

• GDR in the entrance channel of the reaction
• GDR in near Super-Heavy nuclei

Conclusion

224cm Variable Energy Cyclotron; Operating Since 1977

Available Projectile Beams from VECC

Alpha (He2+) : 28 – 60 MeV 5.5 – 7.5 MeV (He+ ): 3.33 MeV Proton : 7 – 20 MeV Deuteron : 25 MeV We plan to provide: Nitrogen (14)  5+, 6+ Oxygen (16)  5+, 6+, 7+ Neon (20)  6+, 7+ Argon (40)  11+, 12+, 13+ Ni (58)  16+ and above Cu (63)  17+ and above Zn (65)  17+ and above

• 162 large BaF2 Detector

elements

• Detector dimensions:

3.5 x 3.5 x 35 cm3

• Fast, quartz window PMT

(29mm, Phillips XP2978)

• Highly Granular & Modular in

nature

• Dedicated CAMAC front end

electronics

• Dedicated Linux based VME

DAQ

• Solid angle coverage ~ 6% of 4

(LAMBDA) Large Area Modular BaF2 Detector Array

• S. Mukhopadhyay et al, NIM A 582 (2007) 603

High Energy Gamma Spectrometer

Experimental Setup (close view)

Individual TOF Individual PSD Dynamic cluster summing Cosmic rejection

A few measurements at VECC K-130 Cyclotron

Experiments done at VEC with 145 & 160 MeV 20Ne beams populating 47V, 32S at high excitations and angular momenta

(using “LAMBDA” photon spectrometer at VECC)

Jacobi shape transition & Super-deformation / orbiting

E (MeV)

5 10 15 20 25 30

Yield/MeV (a.u)

1 2 3

< J > = 28 T = 2.9 MeV

47V

X Axis

1 2 3 4

E (MeV)

10 15 20 25 30

Yield (arb. units) / MeV

1 2 3

T = 2.6 MeV T = 2.82 MeV 145 MeV 160 MeV

32S 32S

20Ne + 27Al  47V 20Ne + 12C  32S

Highly fragmented GDR line-shape

Now when the nucleus is subjected to rotation --- deformation sets in Our aim is to calculate the equilibrium deformation at a given J & T Total free Energy

2 2 1

. ) ( ) , , , (   

zz shell av DLD

I S T E E E T J F     

         

  

        

 i i i i i i i i

f f f f S T e f e f n E 1 ln . 1 ln . ) ( exp 1 . .

1



Where,

ei are the single particle energies Eav is the Strutinsky averaged energy S is Entropy of the system fi are the Fermi occupation nos.  is the chemical potential

At high temperatures (T > 2 MeV), the shell correction is negligible and may be ignored

How to explain such lineshapes

Free energy surfaces were computed in the range, 0 <  < 1 and 0o <  < 60o

0.0 0.2 0.4 0.6 0.8 1.0 10 20 30 40 50 60

10 20 25 28 29 30 33 35 37 40 32

 

27

• blate

triaxial prolate and the minimum of the free energy surfaces corresponds to the equilibrium shape (,) at a particular J and T.

J ()

5 10 15 20 25 30 35 40

• Mom. of Inertia (2/MeV)

8 10 12 14 16 18 20

• blate

triaxial prolate

47V nucleus

undergoing a shape transition

• blate

GDR vibration samples an ensemble of shapes around equilibrium shape An averaging is done around the equilibrium shape with the Boltzman probability exp(-F/T)

 

 

            

     

d d e d d J T E e J T E

T J T F T J T F

. 3 sin . . 3 sin ). , , , ; ( ) , ; (

4 / ) , , , ( 4 / ) , , , (

The averaged GDR strength function due to thermal fluctuations is calculated

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.5 1.0 1.5

• 0.5

0.0 0.5 1.0 1.5

Probablity  cos(+30

• )

 sin(+30

• )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.5 1.0 1.5

• 0.5

0.0 0.5 1.0 1.5

Probablity  c

• s

(  + 3

• )

 s i n (  + 3

• )

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.5 1.0 1.5

• 0.5

0.0 0.5 1.0 1.5

Probablity  cos(+30

• )

 s i n (  + 3

• )

Thermal Fluctuations superimposed

Once we know the equilibrium shape, we can calculate the GDR strength function corresponding to that shape (eq , eq) of the nucleus.

Calculation of GDR strength functions

We know from the systematics,

6 / 1 3 / 1

6 . 20 2 . 31

 

   A A E

GDR GDR

 

, / 1 since and R

GDR 



                 3 2 cos 4 5 exp      

eq eq GDR x

 

                 3 2 cos 4 5 exp      

eq eq GDR y

           

eq eq GDR z

     cos 4 5 exp  

The individual widths are given by,

9 . 1

026 .

i i i

E E E             



 

     

i 2 i 2 2 2 i 2 i 2 TOTAL

E E E E   

  

The resultant total strength function then becomes, we have from Hill-Wheeler parametrization

Jacobi shape transition in 47V



5 10 15 20 25 30

Yield/MeV (a.u)

1 2 3

< J > = 31 T = 2.8 MeV

47V

0.0 0.2 0.4 0.6 0.8 1.0 10 20 30 40 50 60

10 20 25 28 29 30 33 35 37 40 32

 

27

20Ne (160 MeV) + 27Al

Gradual evolution of shape from spherical to

• blate to triaxial to extended prolate with

increasing rotation

47V

GDR vibration couples with the rotation and the strength fn. splits – in general into 5 components (Coriolis splitting at high rotation)

PRC 81 (2010) 061302 (Rapid comm.)

X Axis

1 2 3 4

E (MeV)

10 15 20 25 30

Yield (arb. units) / MeV

1 2 3

T = 2.6 MeV T = 2.82 MeV 145 MeV 160 MeV

32S 32S

Odd nuclear shape (prolate, super-deformed) β ≈ 0.75 , axis ratio ≈ 2:1

Orbiting di-nuclear complex seen directly via GDR

20Ne + 12C  32S

• Phys. Rev. C 81 (2010) 061302 (Rapid comm.)

0.0 0.2 0.4 0.6 0.8 10 20 30 40 50 60

11

 

25 22 21 18 20 19 17 14 8

Hot & rotating Liquid drop calculations fail miserably to describe the GDR strength fn. Indicates a different reaction mechanism

• --- Orbiting !!!

32S

Can bremsstrahlung radiation be observed in Nuclear Fission?

Energy Released = 200 MeV

Coulomb Acceleration Model: This model assumes coulomb acceleration of the two fission fragment from a scission like configuration to infinity .

In the non-relativistic limit,  << 1 Motion of the two fission fragment is confined to one dimensional motion along the fission axis. Thus the relative acceleration is

=

• J. D. Jackson

Energy spectrum, in the non-relativistic limit, of bremsstrahlung produced from the acceleration of the fission fragments. Motion of the fragments can be determined by solving the equation for the two particles under the influence of a repulsive coulomb potential

 is the reduced mass k = z1z2e2 ṙ is the relative velocity E is the energy of the system

2

k x r  

Photon Energy (MeV) 20 40 60 80 100

• No. of Photons/ (fission x MeV)

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

Rmin = Z1Z2e2/E Pre-scission kinetic energy = 25-30 MeV Conservation of Energy (1 - /E) Emission probablity of the bremsstrahlung photons very small. Classical Coulomb acceleration model (non-relativistic)

High Energy Photons from 252Cf

The spectrometer LAMBDA is capable of measuring photons up to ~ 200 MeV with very good efficiency for full energy

Photon Energy (MeV) 20 40 60 80 100

• No. of Photons/ (fission x MeV)

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

Classical bremsstrahlung considering the pre-scission kinetic energies of the fission fragments Physics Letters B 690 (2010) 473

252Cf

Emitted photons from the Spontaneous fission of

Coherent Bremsstrahlung emission observed for the first time (!!!) up to 80 MeV

• - from the Coulomb accelerated

fission fragments in spontaneous fission of 252Cf

Fragment Mass (amu)

90 100 110 120 130 140 150 160

GDR Emission (%)

0.00 0.02 0.04 0.06 0.08

E* (MeV)

10 20 30

• No. of Photons / (Fission x MeV)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 Photon Energy (MeV)

5 10 15 20 25

Yield (arb. units)

1 2

Temperature (MeV)

0.0 0.5 1.0 1.5 2.0 2.5

GDR Width (MeV)

2.5 5.0 7.5 10.0 12.5

Phys Lett B 690 (2010) 473

GDR width from excited fragments of 252Cf

<A> = 117 <T> = 0.68 MeV <M>=117

• Phys. Letts. B 709, 9, (2012)
• Phys. Letts. B 713, 434, (2012)

Critical Temperature Fluctuation Model (CTFM)

This critical behavior is seen for the first time and is explained in terms of the GDR induced quadruple deformation and its competition with the thermal fluctuations Systematic study of the GDR width at low temperature

Temperature (MeV)

0.0 0.5 1.0 1.5 2.0 2.5

GDR Width (MeV)

2.5 5.0 7.5 10.0 12.5

120Sn

GDR Width (MeV)

5 10 5 10 15

Temperature (MeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 5 10

63Cu 120Sn 208Pb

(a) (b) (c) J = 20 J = 15 J = 15

J ( )

20 40 60 80



0.0 0.1 0.2 0.3 0.4

 eq

J ( )

20 40 60 80 GDR Width 8 10 12 14

GDR width does not increase until equilibrium deformation becomes larger than the fluctuations of the deformation (TSF Model)

Critical spin Jc ~ 0.6A5/6

Observed in entire the mass region

TSFM gives excellent description of GDR width as a function of J Angular momentum dependence of GDR width (Similar idea)

X Axis 5 10 15 20 25

1 2 3 4

X Axis 5 10 15 20 25

1 2 3

X Axis 5 10 15 20 25

1 2 3 E (MeV)

5 10 15 20 25

Yield (arb unit) / (0.5 MeV) 1 2 3

X Axis 5 10 15 20 25

1 2 3 E (MeV)

5 10 15 20 25

1 2 3

50 MeV 42 MeV 42 MeV 50 MeV 50 MeV 42 MeV F > 4 F > 4 F = 3 F = 3 F = 2 F = 2

4He + 93Nb  97Tc*

Elab = (28, 35, 42, 50 MeV)

Temperature (MeV) 0.0 0.5 1.0 1.5 2.0 2.5 GDR Width (MeV) 5 10

J = 15

97Tc

1/A 0.005 0.010 0.015 Tc (MeV) 0.8 1.0 1.2 1.4 Tc = 0.7 + 37.5/A

Further verification in different mass region

Experimental Signature for GDR – GQR Coupling at finite Temp --- ???

Physical Review C 91, 044305 (2015) Physics Letters B 731 (2014) 92

97Tc 97Tc

Phonon Damping Model (included Thermal Pairing) Thermal Shape Fluctuation Model (with Pairing Fluctuations) Ground state GDR widths are estimated with the Spreading Width Parameterization given by A. R. Junghans et al, Phys. Lett. B 670 (2008) 200 (0.05 * Egdr^1.6 MeV) and is consistent with the measured values GDR width should vary continuously From its G.S. value with increase in T

Modified Kusnezov parameterization with GDR – GQR coupling included Universal macroscopic description for a complete range of T & J

Yield / MeV No suppression in IVGDR γ - yield. Compared with CASCADE calculation with full mixing IVGDR decay Suppressed Blue-dashed line  CASCADE calculation with full mixing Red line  CASCADE calculation with = 13 keV





Isospin symmetry breaking/restoration in excited nuclei Tz ≠ 0, ΔT = 0,1 allowed transitions Tz = 0, ΔT = 0 forbidden

Degree of isospin mixing can be estimated by observing the isospin forbidden transitions.

E* (MeV) 30 40 50 60 70 2 4 6 8 10

32S 28Si 36Ar theoretical curve

E* (MeV) (KeV) %

29.9 13 ± 8 5.8 ± 3.0

For 32S at 30 MeV excitation Isospin symmetry breaking/restoration in excited nuclei

The result shows mixing increases with a decrease in temperature in accordance with Wilkinson’s prediction Relative importance of the charge symmetry and charge independence breaking forces in nuclear phenomena Correction in the transition matrix element for super-allowed Fermi β-decay. This helps in the proper estimation of the u-quark to d-quark transition matrix element in the Cabibo-Kobayashi-Maskawa (CKM) matrix whose unitarity validates the standard model. Requires mixing at T = 0

 



2 



Plans for the VECC Super-conducting cyclotron

Pre-equilibrium GDR Prompt dipole gamma emission due to entrance channel charge asymmetry

Charge asymmetric collisions forms large amplitude dipole collective motion before complete equilibration (charge)



 

2 1 2 2 1 1 2 1

R R Z N Z N A Z Z D           

Initial dipole moment  Dipole

• scillation 

Statistical CN - GDR

Excess GDR photon yield – when compared with a similar but more charge symmetric system

Density plots projected on reaction plane for central collisions (TDHF)

PRL 86 (2001) 2971.

Strong effect for very asymmetric target / projectile combination.

Plans with Super-conducting Cyclotron ---- At still higher energies

Pre-equilibrium GDR

40Ca + 100Mo  N/Z ratio -- 1 : 1.38 36S + 104Pd  N/Z ratio -- 1.25 : 1.26 ≈ 1:1

Same CN 140Sm* (N/Z = 1.26) is formed

Filbotte et al, PRL 77, 1448 (1996), Pierroutsakou et al.,PR C71, 054605 (2005)

• information on the charge equilibration in

relation to the reaction mechanism;

• information on the damping of the dipole

mode;

• information on the symmetry energy of

the nuclear matter at lower densities than the saturation one

Near SHE population & their GDR characteristics

Very heavy nuclei [ Z > 105, A > 250 ] may be populated at high excitation and their GDR characteristics studied ( T ~ 2.5 – 3 MeV) These are highly fissile systems Fission process slows down as excitation increases – well known At still higher excitation it further slows down so that

• -- Prefission GDR γ emission competes with fission,
• -- possible to see GDR decay photons cleanly (using difference method)

Photon Energy (MeV)

MeV/A 15 & 10.5 at

272 108 40 232

Hs Ar Th  

Tveter, PRL 76, 1025 (1996)