SPIN-PARITIES AND HALF LIVES OF 257 No AND ITS α-decay DAUGHTER 253 Fm

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1 NUCLEAR PHYSICS SPIN-PARITIES AND HALF LIVES OF 5 No AND ITS α-decay DAUGHTER 5 Fm P. ROY CHOWDHURY, D. N. BASU Saha Institute of Nuclear Physics, Variable Energy Cyclotron Centre, /AF Bidhan Nagar, Kolkata , India Received March 6, 006 Recently measured lifetimes of the favored α decays from 5 No were calculated using the quantum mechanical tunneling within WKB approximation using microscopic nuclear potentials. Results obtained assuming previously assigned parent spin of ( ) and newly assigned configuration [6] have been compared. Hindrance factors for the favored decays were compared with the calculated hindrances using higher angular momenta transfers. Although the calculations substantiate the findings, yet it makes the spin-parity assignment of for the ground state of 5 No less definite.. INTRODUCTION In a recent experimental work [], lifetimes of the favored α decays from 5 No were measured and the spin-parities of the excited states (e.s.) in 5 Fm fed by the α decays of 5 No were claimed to be identified on the basis of the measured internal conversion coefficients. The [6] configuration were assigned to the ground state (g.s.) of 5 No as well as to the 4. kev level in 5 Fm. The previously assigned g.s. spin for 5 No was ( ) []. In the present work, attempt was made to ascertain spin and parity of 5 No g.s. from a comparison of measured and calculated α -decay half-lives of 5 No. The α-decay half-lives of 5 No were calculated using the quantum mechanical tunneling within WKB approximation using Coulomb, centrifugal barriers and nuclear potential obtained by folding a density dependent MY effective interaction.. FORMALISM In the present work, the decay Q α values for the favored decays were calculated from the measured α particle kinetic energy (K.E.) E α using standard partha.roychowdhury@saha.ac.in Rom. Journ. Phys., Vol. 5, Nos. 9 0, P , Bucharest, 006

2 854 P. Roy Chowdhury, D. N. Basu recoil correction and the electron shielding correction in a systematic manner as suggested by Perlman and Rasmussen []. The Q α value for α decay from g.s. of 5 No to the g.s. of 5 Fm was calculated using atomic mass excesses from the most recent experimental mass table [4]. Q α values, thus obtained, have then been used to calculate lifetimes of the favored as well as g.s. to g.s. α decays from 5 No using the quantum mechanical tunneling within WKB approximation using microscopic nuclear potentials [5]. The nuclear interaction potentials required to describe these α decay processes have been calculated by double folding the density distribution functions of the α particle and the daughter nucleus with density dependent MYeffective interaction. The microscopic α -nucleus potential thus obtained, along with the Coulomb interaction potential and the minimum centrifugal barrier required for the spin-parity conservation, have been used for the lifetime calculations of these α disintegration processes. Spherical charge distributions have been used for calculating the Coulomb interaction potentials [5]. These calculations provide good estimates for the observed α decay lifetimes of nuclei including superheavies [6, ]. The decay Q α values for the favored decays can be obtained from the measured α particle K.E. E α using the following expression Ap Q / / α = Eα (65. Z ) 0 6 p Zp MeV () Ap 4 where the first term is the standard recoil correction and the second term is an electron shielding correction in a systematic manner as suggested by Perlman and Rasmussen []. But for decays to the g.s. of daughter nucleus for which α particle K.E. has not been measured can be calculated from the g.s. masses using the following relationship Q= M ( M M ) () α which being positive allows decay to the g.s., where M, M α and M d are the atomic masses of the parent nucleus, the emitted α -particle and the residual daughter nucleus, respectively, expressed in the units of energy. d. CALCULATIONS AND RESULTS The results of the present calculations are presented in Table. The Q α value of MeV calculated for the transition to g.s. of 5 Fm from the experimental mass excesses [4, 8] which should be more but turns out to be less than the the value of 8.496() MeV derived [] from the measured α particle K.E. for transition to the e.s. at. kev. This experimental result for E α appears

3 5 No and its α-decay daughter 5 Fm 855 Table Calculated half lives for α decays from the g.s. of 5 No to different e.s. and to the g.s. of 5 Fm. Calculated Q α values have been derived from measured α particle K.E. E α using eqn. () [] whereas the Q α value for α decay to the g.s. has been calculated from the atomic masses [4, 8] using eqn. (). The minimum angular momenta l carried away by the α particles have been decided by the spin-parity coservation. Uncertanties in the calculated half lives arising from the experimental uncertainties in the Q α values and uncertain spins have been provided within parentheses g.s. 5 No g.s./e.s. 5 Fm g.s./e.s. 5 Fm Measured E α Derived T th Q / α J π Energy [MeV] J π MeV MeV s ( ) [] 0.0 g.s. ( ) [] 0.0 g.s [8] [4] [8].95 [] 0.0 g.s [4] (6) 8.94(6) 5.68() 0 ( ) [] (6) 8.94(6) 8.94() ( ) 8.() 8.496().8(8) 0 ( ) [] 0.0 ( ) [] 0.0 ( ) 8.() 8.496().48(0) (?) 8.() 8.496() 55.4(9) 4 to be slightly erroneous. However, it is interesting to note that if only the recoil correction is considered then the result is 8.455() MeV which is almost within the acceptable limits. The theoretical results for the half-lives are often underestimated because the centrifugal barrier required for the spin-parity conservation could not be taken into account due to non availability of the spin-parities of the parent or the daughter/decay chain nuclei. The term ll ( ) /( μr ), where μ is the reduced mass and r is the distance between α and daughter nuclei, represents the additional centrifugal contribution to the barrier that acts to reduce the tunneling probability if the angular momentum carried by the α-particle is non-zero. Hindrance factor which is defined as the ratio of the experimental mean life τ expt. (or experimental half life) to the theoretical mean life τ th. (or theoretical half life) is therefore larger than unity since the decay involving a change in angular momentum can be strongly hindered by the centrifugal barrier. The hindrance factor (HF) HF =τ /τ, () expt. th. l

4 856 P. Roy Chowdhury, D. N. Basu 4 however, can also be different from unity because of other factors (such as nuclear deformations) not considered in theoretical calculations. But these effects are much smaller. The total mean life τ (or half life T / ) can be obtained from the partial mean lives τ, τ, τ, τ, τ (or partial half lives) using = τ τ τ τ τ 4 which suggests that the total lifetime is always less than or equal to any of the partial lifetimes. (4) 4. DISCUSSION As the spin-parity of the state at. kev of 5 Fm is uncertain [], transitions other than l = 0 may be possible. But angular momentum l = carried away by the α particle for transition to the 4. kev state is not possible. Therefore, transition to. kev state with half life higher than.8(8) s with HF of or 8 may be possible but the half life for the transition to 4. kev state can not be more than 5.68() s since spin-parity of this state has been claimed to be definite []. Since eqn. (4) shows that the total half life must be less than the most favored decay lifetime, present calculations somewhat underestimates the measured half life of 4.5(5) s. But certainly the earlier less definite assignment of the spin-parity of [] for the 5 No suggests g.s. to g.s. α emissions less favored since then the spin-parity conservation forces 4 units of angular momentum to be carried away by the α particle for transition to the g.s., resulting a too high lifetime of about 0 s. For transitions to the states at 4. kev and. kev with spin-parity, from a state with, the spin-parity conservation forces a minimum of units of angular momentum to be carried away by the α particle, resulting the half-lives of 8.94 s and.48 s respectively. Moreover, half life of the.48 s may also be different as the spin ( ) of the. kev level is also somewhat uncertain. The ENSDF half life value of 5() s for the favored α decay to 5 Fm going to a level at 00 kev is reasonably close to the value of 8.94() s calculated assuming for the spin-parity for the g.s. of 5 No. Half lives of 8.94 s, 55.4 s (?) and.95 s may result in a measured half life of about 5 s. Therefore, from the measured α decay half life of 4.5(5) s, it is not possible to rule out the possibility of the g.s. spin-parity of for the 5 No.

5 5 5 No and its α-decay daughter 5 Fm SUMMARY AND CONCLUSION An attempt is made to ascertain spin and parity of the 5 No g.s. from a comparison of measured and calculated α -decay half-lives of 5 No. The new g.s. spin-parity of assigned for the 5 No obtained in ref. [] are based on conversion coefficients and conversion electron spectra measured in coincidence with α rays. From the measured α decay half life of 4.5(5) s, it is not possible to rule out the possibility of the previously assigned g.s. spin-parity of for the 5 No. Moreover, the ENSDF half life value of 5() s for the favored α decay to 5 Fm going to a level at 00 kev is reasonably close to the value of 8.94() s calculated assuming for the spin-parity for the g.s. of 5 No which makes the g.s. spin-parity of for the 5 No to be more likely. REFERENCES. M. Asai et al., Phys. Rev. Lett. 95, 050 (005).. R. B. Firestone and V. S. Shirley (Eds.), Table of Isotopes, eighth edition, published by John Wiley and sons, Inc. (999).. I. Perlman and J. O. Rasmussen, Handb. Phys. XLII, 09 (95). 4. G. Audi, A. H. Wapstra and C. Thibault, Nucl. Phys. A 9, (00). 5. D. N. Basu, Phys. Letts. B 566, 90 (00). 6. D. N. Basu, Jour. Phys. G 0, B5 (004).. P. Roy Chowdhury, C. Samanta and D. N. Basu, Phys. Rev. C, 046 (006). 8. W. D. Myers and W. J. Swiatecki, Lawrence Berkeley Laboratory preprint LBL-680 (994); Nucl. Phys. A 60, 4 (996).

arxiv:nucl-th/ v4 30 Jun 2005

arxiv:nucl-th/ v4 30 Jun 2005 Modified Bethe-Weizsäcker mass formula with isotonic shift and new driplines P. Roy Chowdhury 1, C. Samanta 1,2 1 Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700 064, India 2 Physics