Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 1 V.A. Chetvertkova, B.S. Ishkhanov, V.N. Orlin, V.V. Varlamov Skobeltsyn Institute of Nuclear Physics and Physics Faculty, Lomonosov Moscow State University, Moscow, Russia EXPERIMENTAL-THEORETICAL EVALUATION OF PARTIAL PHOTONEUTRON REACTIONS  ( ,n) AND  ( ,2n) CROSS SECTIONS FOR Sn ISOTOPES Title

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 2 Giant Dipole Resonance (for example, 119 Sn) ( ,abs) = ( ,n) + ( ,2n) + ( ,3n) +…+ ( ,p) + … + ( ,f) = ( ,sn) + ( ,p) + … + ( ,f) ( ,xn) = ( ,n) + 2( ,2n) + 3( ,3n) +… Balance of cross sections of reactions with several (primarily 1 and 2) outgoing neutrons is very important characteristic of nucleus photodisintegration process: competition of various decay channels; competition of direct and statistical processes; effects of GDR configurational splitting; effects of GDR isospin splitting; ….many others. n-2n-3n

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 3 Thresholds Energy thresholds of various reactios are close to each other, moreover for 112,114,116 Sn B p < B n (B np < B 2n )  ( ,xn) =  ( ,n) + 2  ( ,2n) + …+  ( ,np) +  ( ,n2p) + 2  ( ,2np) +...    ( ,nX) + 2  ( ,2nX) +...

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 4 Disagreements Bremsstrahlung experiments: where  (E) is cross section of reaction  ( ,xn) with threshold E th at photon energy E; W(E m,E) is bremsstrahlung spectrum with end-poin energy E m ;  is normalization constant.  ( ,nX) contribution into  ( ,xn) determined using statistical theory. Quasimonoenergetical annihilation photons experiments - 3 steps: 1) measurement of yield Y e+ (E j ) resulted from sum of photons from positron annihilation and bremsstrahlung; 2) measurement of yield Y e- (E j ) resulted from electron bremsstrahlung; 3)  (E)  Y e+ (E j ) - Y e- (E j ) = Y(E j ). Majority of data - Livermore (USA) and Saclay (France) - different methods of neutrons outgoing from reactions  ( ,nX) and ( ,2nX) multiplicity sorting. Significant systematical disagreemrnts!

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) Sn-n-2n 120 Sn( ,nX) 120 Sn( ,2nX) – Livermore QMA-data: close to evaluated ones – Saclay QMA-data: far from evaluated ones – Moscow BRA- data: scattered around evaluated ones – evaluated - data (will be explained further)

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 6 “( ,nX) – ( ,2nX)” – Fig. Squares - - ratios for ( ,nX) reactions – are larger than 1.0 Triangles -  - ratios for ( ,2nX) reactions – are smaller than 1.0. Graphical presentation of ( ,nX) – ( ,2nX) disagreements between Saclay and Livermore data 51 V, 75 As, 89 Y, 90 Zr, 115 In, 116,117,118,120,124 Sn, 127 I, 133 Cs, 159 Tb, 165 Ho, 181 Ta, 197 Au, 208 Pb, 232 Th, 238 U

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 7 Table Clear systematical Saclay/Livermore disagreements > 1 < 1

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 8 Total photoneutron reaction cross section in GDR energy region ( ,xn) = ( ,nX) + 2( ,2nX). Ratio R (“Saclay/Livermore” normalization) for all reactions cross sections R =  xn S /  xn L =  n S /  n L =  2n S /  2n L = (  n S + 2  2n S )/(  n L + 2  2n L ),  xn S = (  n S + 2  2n S ) = R  xn L = R(  n L + 2  2n L ). Saclay corrected  2n S * must be equal to Livermore corrected:  2n L * = R  2n L, therefore:  2n L * =  2n S * = R  2n L =  2n S + 1/2(  n S - R  n L ). Saclay ( ,n) reaction cross section part 1/2(  n S - R  n L ) is “transmitted back” to Saclay ( ,2n) reaction cross section  2n S. “n-2n” correction formulae

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 9 116,118,120 Sn ( ,nX) ( ,2nX) 116 Sn 118 Sn 120 Sn Part of Saclay ( ,nX) reaction cross section transported back into ( ,2nX) cross section Corrected Saclay ( ,nX) reaction cross section – error bars (line – uncorrected data). In principle that’s possible to put Saclay’s data into consistency with Livermore’sones using correction of multiplicity sorting

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) Sn-n Livermore data for  ( ,nX): negative cross section values, very strange bump at higher energies 0 Definite multiplicity sorting errors 116 Sn

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 11 Summary Short summary: there are a lot of data for partial photoneutron reaction cross section data; significant systematical disagreements were found out; many different methods were used, all of them have definite shortcomings; an unuque treatment is needed.

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 12 New treatment New experimental-theoretical treatment of the evaluation of partial photoneutron reactions  ( ,nX) and  ( ,2nX) cross sections: initial data - experimental  exp ( ,xn) reaction cross sections that are free of shortcomings of meatods of neutron multiplicity sorting; separation of partial cross sections using theoretically calculated transitional function of multiplicity F theor =  theor ( ,2nX) /  theor ( ,xn) =  theor ( ,2nX) / [  theor ( ,nX) + 2  theor ( ,2nX)]  eval ( ,2nX) = F theor  exp ( ,xn)  eval ( ,nX) = (1 - 2F theor )  exp ( ,xn)

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 13 Model ( ( B.S.Ishkhanov, V.N.Orlin. Physics of Particles and Nuclei 38, 232 (2007), ): Physics of Atomic Nuclei 71, 493 (2008 )): Model semiclassical exiton preequilibrium model of photonuclear reaction based on the Fermi gas densities; effects of nucleus deformation; effects of Giant Dipole Resonance isospin splitting. M.B. Chadwick et al., Phys. Rev. C 44, 814 (1991).

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 14 Competition 124 Sn ( ,0pkn) ( ,1pkn) ( ,2pkn) Various decay channels competition

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 15 F B 3n tresholds of ( ,3n) reactions E, MeV F theor =  theor ( ,2nX) / [  theor ( ,nX) + 2  theor ( ,2nX)], arb. units 0.5 Main features: threshold behavior; 0.5 limit for absolue value - that is division of  ( ,2nX) to itself twised (with small addition of  ( ,nX)); weak decrease at B 3n because of  ( ,3n) contribution

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) Sn-n Livermore data for  ( ,nX): negative cross section values and strange bump at high energies - neutron multiplicity sorting effects 0 Definite multiplicity sorting errors 116 Sn There are definite discrepancies in neutron multiplicity sorting.  B 2n  B 3n 0.5  ( ,2nX) F  __________________ < 0.5  ( ,nX) + 2  ( ,2nX)

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) ,124 Sn There are definite discrepancies in neutron multiplicity sorting 124 Sn  B 2n  B 3n 120 Sn  B 3n  B 2n This situation is near normalThis situation is not normal

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 18 Eval-data  ( ,nX) and  ( ,2nX) experimental-theoretical evaluation: calculation of theoretical cross sections  theor ( ,nX) and  theor ( ,2nX); calculation of theoretical sum cross section  theor ( ,xn) =  theor ( ,nX) + 2  theor ( ,2nX); calculation of theoretical transition multiplicity function F theor =  theor ( ,2nX) /  theor ( ,xn) =  theor ( ,2nX) / [  theor ( ,nX) + 2  theor ( ,2nX)]; evaluation of partial reaction cross sections  eval ( ,2nX) = F theor  exp ( ,xn) and  eval ( ,nX) = (1 - 2F theor )  exp ( ,xn) for each individual experiment; joint evaluation summation  eval-joint ( ,sn) =  eval-joint ( ,nX) +  eval-joint ( ,2nX)   ( ,abs).

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 19 Agreements 116 Sn 117 Sn 124 S n In general there are agreements between data obtained by 4 different ways: 1) bremsstrahlung photons and statistical theory; 2) quasimonoenergetical photons and neutron multiplicity sorting method of Livermore; 3) quasimonoenergetical photons and neutron multiplicity sorting method of Saclay; 4) new experimental-theoretical evaluation.

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 20 Disagreements - Saclay In detailes: clear disagreements were revealed for energies higher B 2n for Saclay multiplicity sorting data for 3 isotopes 116 Sn 118 Sn 120 Sn  eval ( ,2nX)  eval ( ,nX)

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 21 Disagreements Sn In detailes: clear disagreements were revealed for energies higher B 2n for Livermore multiplicity sorting data for 116 Sn 116 Sn  eval ( ,nX)  eval ( ,2nX) F increasing ->  ( ,nX) decreasing F decreasing ->  ( ,nX) increasing

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 22 Disagreements Sn In detailes: clear disagreements were revealed for energies higher B 2n for Livermore multiplicity sorting data for 124 Sn 124 Sn  eval ( ,nX)  eval ( ,2nX) F decreasing ->  ( ,2nX) decreasing F decreasing ->  ( ,nX) increasing

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 23 Disagreements - BR In detailes: disagreements were revealed for energies higher B 2n for data obtained using bremsstrahlung for 114,116,117,119 Sn. Maybe that is the result of large direct processes contributions into the GDR B.L. Berman, S.S. Fultz. Measurements of the Giant Dipole Resonance with Monoenergetic Photons. Rev. Mod. Phys V. 47. P. 713: that is for 117 Sn

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 24 Important results So: 1) proposed experimental-theoretical evaluation gives results that are generalally in agreement with experimental data; 2) evaluated data are in good agreement with data obtained using bremsstrahlung and using qiasimonoenergetical photons at Livermore; 3) evaluated data are not in good agreement with data obtained at Saclay; 4) each case of clear disagreements can be explained by definite shortcomings of neutron multiplicity sorting procedures used; 5) therefore evaluated data could be interpreted as free of shortomings discussed.

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 25 ( ,nX) - ( ,2nX)  ( ,nX) is decreasing, but  ( ,2nX) is increasing because (Em – B 2n ) decreasing. Clear smooth behavior of both partial reactions cross sections with A changing

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 26 Main param. Main GDR parameters comparison for  ( ,sn)   ( ,abs): good agreement in energy position, absolute value and shape Main A-dependencies (112  124): E m shifts to smaller values;  shifts to smallr values (till magic number N = 82).  m is about constant.

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 27 Integr. cross sect. Integrated cross sections comparison for  ( ,sn)   ( ,abs) GDR (( ,sn)   ( ,abs)) integrated cross section is practically constant in 112 Sn  124 Sn.

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 28 Summary Partial photoneutron reactions cross sections  ( ,nX) and  ( ,2nX) data for 112,114,116,117,118,119,120,122,124 Sn isotopes were systematically analysed. Clear systematical disagreements between data obtained using various experimental methods were revealed and interpreted as results of shortcomings of neutron multiplicity sorting procedures. The experimental-theoretical method free from neutron multiplicity sorting problems was proposed using experimental data only for total neutron yield reaction cross section  exp ( ,xn) =  exp ( ,nX) + 2  exp ( ,2nX). Contributions of partial reaction cross sections into total one was evaluated using the theoretically calculated transitional multiplicity function F theor =  theor ( ,2nX) /  theor ( ,xn):  eval ( ,2nX) = F theor  exp ( ,xn)  eval ( ,nX) = (1 - 2 F theor )  exp ( ,xn). In general good agreement was obtained between evaluated data and experimental ones with the exception of several cases of Saclay data. Using jointly evaluated partial reaction cross sections  eval ( ,2nX) and  eval ( ,nX) total  eval ( ,sn) =  eval ( ,nX) +  eval ( ,2nX)   ( ,abs) was obtained and analysed for all 9 Sn isotopes. Summary

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 29 Thanks EXPERIMENTAL-THEORETICAL EVALUATION OF PARTIAL PHOTONEUTRON REACTIONS  ( ,n) AND  ( ,2n) CROSS SECTIONS FOR Sn ISOTOPES THANKS A LOT FOR ATTENTION !

Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics V.Varlamov, EMIN-2009 (21 – 26 September) 30 Theory S emiclassical exiton preequilibrium model of photonuclear reaction based on the Fermi gas densities and taking into account the effects of nucleus deformation and of GDR isospin splitting. Bohr description of  ( ,lpkn):  i - one of 4 components (2 isospins - T 0 and T and 2 directions of vibration),  GDR - Lorenz lines with W - decay probabilities (recurrent): Theory where