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

GDR Studies at VECC Facility Sudhee R. Banerjee Variable Energy Cyclotron Centre, Kolkata, India

Outline Introduction A few measurements at VECC K-130 Cyclotron with LAMBDA photon spectrometer -Jacobi shape transition -Super-deformation in 32 S – orbiting or clustering? -Coherent bremsstrahlung in 252 Cf spontaneous fission -Evolution of GDR widths with Temperature -GDR strengths in 252 Cf 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 We plan to provide: Alpha (He 2+ ) : 28 – 60 MeV 5.5 – 7.5 MeV Nitrogen (14)  5+, 6+ (He + ): 3.33 MeV Oxygen (16)  5+, 6+, 7+ Proton : 7 – 20 MeV Neon (20)  6+, 7+ Deuteron : 25 MeV Argon (40)  11+, 12+, 13+ Ni (58)  16+ and above Cu (63)  17+ and above Zn (65)  17+ and above

High Energy Gamma Spectrometer  162 large BaF 2 Detector (LAMBDA) Large Area elements Modular BaF 2 Detector Array  Detector dimensions: 3.5 x 3.5 x 35 cm 3  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  S. Mukhopadhyay et al, NIM A 582 (2007) 603

Experimental Setup (close view)

Individual TOF Individual PSD Dynamic cluster summing Cosmic rejection

A few measurements at VECC K-130 Cyclotron

Jacobi shape transition & Super-deformation / orbiting Experiments done at VEC with 145 & 160 MeV 20 Ne beams populating 47 V, 32 S at high excitations and angular momenta (using “LAMBDA” photon spectrometer at VECC) 20 Ne + 27 Al  47 V 20 Ne + 12 C  32 S 4 T = 2.6 MeV 145 MeV < J > = 28 32 S 47 V 3 3 T = 2.9 MeV Yield/MeV (a.u) Yield (arb. units) / MeV 2 2 1 T = 2.82 MeV 160 MeV X Axis 1 32 S 3 2 0 5 10 15 20 25 30 1 E  (MeV) 0 10 15 20 25 30 E  (MeV) Highly fragmented GDR line-shape

How to explain such lineshapes 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 1 F ( , , J , T ) E ( E E ) T . S I DLD av shell zz 2 e i are the single particle energies   Where, E n . f . e i i E av is the Strutinsky averaged energy          1 f 1 exp ( e ) T S is Entropy of the system i i              S f . ln f 1 f . ln 1 f f i are the Fermi occupation nos. i i i i  is the chemical potential At high temperatures (T > 2 MeV), the shell correction is negligible and may be ignored

Free energy surfaces were computed in the range, 0 <  < 1 and 0 o <  < 60 o and the minimum of the free energy surfaces corresponds to the equilibrium shape (  ,  ) at a particular J and T. 47 V nucleus undergoing a shape transition triaxial 60 50 20 oblate oblate triaxial  40 Mom. of Inertia (  2 /MeV) 18 16 30 14 prolate 20 27 28 12 oblate 25 29 30 10 20 32 10 33 prolate 10 8 35 37 40 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 35 40  J (  )

Thermal Fluctuations superimposed 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) The averaged GDR strength function due to thermal fluctuations is calculated            F ( , , T , J ) / T 4 e ( E ; , , T , J ). sin 3 d . d    ( E ; T , J )          F ( , , T , J ) / T 4 e . sin 3 d . d 1.2 1.2 1.2 1.0 1.0 1.0 0.8 0.8 0.8 Probablity Probablity Probablity 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 0.5 1.5 1.5 0.5  0.5 1.5 1.0  cos(  +30 1.0 c 1.0 o 1.0  cos(  +30 s 1.0  ( 0.5 o ) 0.5 1.0 + o ) 0 3 3 0 1.5 0 o ) + 3  1.5 0.5 o ) o ) 0.0  + ( 0.0  sin(  +30 n ( i n s 1.5  i o ) s  0.0 -0.5 -0.5 -0.5

Calculation of GDR strength functions Once we know the equilibrium shape, we can calculate the GDR strength function corresponding to that shape (  eq ,  eq ) of the nucleus.       1 / 3 1 / 6  We know from the systematics, E 31 . 2 A 20 . 6 A GDR GDR  GDR  and since 1 / R , we have from Hill-Wheeler parametrization      5 2              exp cos   x GDR  eq eq The individual widths are given by,   4 3        E           5 2 1 . 9   i        0 . 026 E       exp cos i 0 i   y GDR eq eq    E   4 3   0   5           exp cos   z GDR  eq eq 4     2 E    The resultant total strength  i   function then becomes, TOTAL 2     2 2 2 2 E E E i   i i

Jacobi shape transition in 47 V 60 50 47 V 20 Ne (160 MeV) + 27 Al  40 30 Gradual evolution of shape from spherical to oblate to triaxial to extended prolate with 20 27 28 25 29 30 increasing rotation 10 20 32 33 10 35 37 40 0 0 0.0 0.2 0.4 0.6 0.8 1.0 GDR vibration couples with the  rotation and the strength fn. splits < J > = 31 – in general into 5 components 47 V 3 T = 2.8 MeV (Coriolis splitting at high rotation) Yield/MeV (a.u) 2 1 PRC 81 (2010) 061302 (Rapid comm.) 0 5 10 15 20 25 30 

Orbiting di-nuclear complex seen directly via GDR 20 Ne + 12 C  32 S 60 50 4 32 S T = 2.6 MeV 145 MeV  40 32 S 3 30 2 Yield (arb. units) / MeV 17 20 18 14 19 20 11 21 10 1 22 8 25 T = 2.82 MeV 160 MeV X Axis 0 0 32 S 3 0.0 0.2 0.4 0.6 0.8  2 Odd nuclear shape (prolate, super-deformed) 1 β ≈ 0.75 , axis ratio ≈ 2:1 0 Hot & rotating Liquid drop calculations fail 10 15 20 25 30 E  (MeV) miserably to describe the GDR strength fn. Phys. Rev. C 81 (2010) 061302 (Rapid comm.) Indicates a different reaction mechanism ---- Orbiting !!!

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 . J. D. Jackson 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 =

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 = z 1 z 2 e 2 ṙ is the relative velocity k   x E is the energy of the system 2 r

10 -1 Classical Coulomb acceleration model (non-relativistic) 10 -2 No. of Photons/ (fission x MeV) 10 -3 R min = Z 1 Z 2 e 2 /E 10 -4 Pre-scission kinetic 10 -5 energy = 25-30 MeV Conservation of Energy 10 -6 (1 -   /E) 10 -7 Emission probablity of the 10 -8 bremsstrahlung photons very small. 10 -9 20 40 60 80 100 Photon Energy (MeV)

High Energy Photons from 252 Cf 10 -1 Coherent Bremsstrahlung emission observed for the first time (!!!) up to 80 MeV 10 -2 -- from the Coulomb accelerated No. of Photons/ (fission x MeV) Emitted photons from the fission fragments in spontaneous 10 -3 Spontaneous fission of fission of 252 Cf 10 -4 252 Cf Classical bremsstrahlung considering 10 -5 the pre-scission kinetic energies of the fission fragments 10 -6 Physics Letters B 690 (2010) 473 10 -7 10 -8 The spectrometer LAMBDA is capable of measuring photons up to ~ 200 MeV with 10 -9 very good efficiency for full energy 20 40 60 80 100 Photon Energy (MeV)

GDR width from excited fragments of 252 Cf 30 10 -1 No. of Photons / (Fission x MeV) 20 E* (MeV) 10 -2 10 10 -3 0 10 -4 GDR Emission (%) 0.08 <A> = 117 0.06 10 -5 0.04 0.02 10 -6 0.00 90 100 110 120 130 140 150 160 10 -7 Fragment Mass (amu) Yield (arb. units) 2 12.5 <T> = 0.68 MeV <M>=117 GDR Width (MeV) 10.0 1 7.5 5.0 0 2.5 5 10 15 20 25 0.0 0.5 1.0 1.5 2.0 2.5 Photon Energy (MeV) Temperature (MeV) Phys Lett B 690 (2010) 473