The variation of E(2 + 1 ) of 134−140 Sn calculated with empirical SMPN interaction has striking similarity with that of experimental E(2 + 1 ) of even-even 18−22 O and 42−48 Ca, showing clearly that N=84-88 spectra exhibit the effect of gradual filling up of ν(2f 7/2 ) orbital which finally culminates in a new shell closure at N=90. Realistic two-body interaction CWG does not show this feature. Spin-tensor decomposition of SMPN and CWG interactions and variation of their components with valence neutron number reveals that the origin of the shell closure at 140 Snlies in the three body effects. Calculations with CWG3, which is obtained by including a simple three-body monopole term in the CWG interaction, predict decreasing E(2 Brown and Richter [8] have framed a generalised new rule for magic numbers, valid specially for lighter nuclei. For heavier nuclei, experimental production of neutron rich isotopes are more difficult. There are severe limitations in acquiring spectroscopic information on them due to their low production rates and lifetimes. However, the shell evolution for neutron -rich nuclei above the doubly magic 132 Sn core is recently a topic of great interest. The Sn isotopes in particular, pose many interesting problems [5,[9][10][11][12][13][14][15] in the study of evolution of nuclear structure with increasing neutron number.The near constancy of the first 2 + energy of Sn isotopes for A=102 to 130 at ≃ 1.2 MeV is a text book example for seniority conserved spectra [16]. But the two valence neutron isotope of Sn just above 132 Sn, i.e., 134 Sn, shows a sudden depression in 2 + 1 energy to 726 keV. This depressed energy is not only interesting from the point of view of nuclear structure [17], it should also have an important implication for the r-process scenario [15].Large basis untruncated shell model (SM) calculations have been done in the valence space consisting of π(1g 7/2 ,2d 5/2 , 2d 3/2 , 3s 1/2 , 1h 11/2 ) and ν(1h 9/2 , 2f 7/2 , 2f 5/2 , 3p 3/2 ,3p 1/2 , 1i 13/2 ) orbitals above the 132 Sn core using both realistic CWG [9,10,12] [10,15,17]. It has been shown in Ref.[10] that this non-constancy of E(2 + 1 ) in Sn isotopes above 132 Sn is a strong possibility. The prediction for dramatic decrease of the E(2 + 1 ) of neutron-rich Sn with increasing neutron number for N=84-88 using SMPN interaction was considered [10] to be an effect showing weakening of the Z=50 shell gap. But the new result, which we report in this letter, on 140 Sn, its high 2 + 1 energy and its comparison with examples from other neutron -rich domains clearly show that N=84-88 spectra with SMPN show the effect of gradual filling up of ν(2f 7/2 ) orbital which finally culminates in a new shell closure at N=90. We show that the realistic CWG predicts similar results, that is decreasing 2 + 1 energies and a shell closure at 140 Sn if three body effects are included in it.The results for the E(2 + 1 ) energies of isotopes of Sn for A=134-140 have been shown in Fig.1 as a function
Using recent experimental information for 132 Sn region, an empirical Hamiltonian is obtained by some modifications of a Hamiltonian (CW5082) originally derived from the 208 Pb region. Shell model calculations with the new Hamiltonian shows remarkable improvement in the predictive power when compared with the available experimental results. It overcomes many limitations of the CW5082 Hamiltonian in this region, specially for N≥84 isotones. The calculated level spectra and B(E2) values with the new Hamiltonian, also compare well with the available results calculated with the CD-Bonn and SKX Hamiltonians, reflecting consistency in the wave function structure at least in the low-lying regions. Interesting behaviour of effective charges is revealed in this region. It is shown that a drastic reduction of proton effective charge is necessary for obtaining B(E2) values for the N=84 isotones. Neutron effective charge is found to be in the range (0.62 -0.72)e. We predict the spectroscopic properties of 135,136 Sn not yet known experimentally. Further improvement of the modified Hamiltonian is also initiated. PACS. 21.60.Cs Shell model -21.10.-k Properties of nuclei, nuclear energy levels -23.20.-g Electromagnetic transitions 27.60.+j 90 ≤ A ≤ 149Send offprint requests to: M. Saha Sarkar Correspondence to: mss@anp.saha.ernet.in
Photospallationyieldsfrom '"Au, "®La, '"Cs, '"I, "Co and ''V were analyzed using iterative non-Iinear least-squares fits to Rudstam's five-parameter (P, ä, R, S and T) CDMD formula which was modified to include the corrections of isobaric precursor decays. The expressions for the parameters P and a obtained in the present analysis were found to be applicable to 51 ^ g 133 and difTerent at Eo ^ 600 MeV, 300 g £o g 600 MeV, and possibly 100g£'og300 MeV. For the heavier targets (A, ^ 140), the P values appear to be smaller and the o-larger than the predictions of the proposed expressions. The parameter R was confirmed to be expressed as /? = d'A and the new values of ef and e' have been proposed. The values of 5 and T are essentially the same as those previously reported by Jonsson and Lindgren. The yields of the products near the targets of 51 g . 4, ^ 197, from (v,xn) reactions at Eg ^ 300 MeV or possibly Eo ^ threshold, were found to be expressed as a function of A, and X. Implications of the newly derived expressions are discussed in the light of reaction mechanism, comparing with those of hadron reactions.
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