Theoretical study on the properties of some superheavy nuclei

ELSEVIER

Nuclear

Physics

A722

(2003)

543c-547~ www.elsevier.com/locate/npe

Theoretical

study

on the properties

of some superheavy

nuclei

Zhongzhou Rena*, Fei Tai ‘, Ding-Han Chen”, H. Y. Zhangb, W. Q. Shenb “Department of Physics, Nanjing University, Nanjing 210008, China bShanghai Institute of Nuclear Research, China Academy of Science, Shanghai 201800, China The structures of some superheavy nuclei are investigated using self-consistent relativistic mean-field (RMF) model. The calculated binding energies and alpha-decay energies are in good agreement with experimental data. The theoretical lifetime reasonably agrees with the data. The properties of some unknown superheavy nuclei are predicted. A discussion on the deformed shell around Z=108 is made. 1. INTRODUCTION Recent progress on superheavy elements attracts both theoreticians and experimenters in nuclear physics [l-9]. Among the newly discovered superheavy elements, there is no argument on the element Z=llO because it was produced by GSI, Berkeley, and Dubna [1,2,4,5]. All these experiments lead to that four nuclides 267,26g,271,273110 of Z=llO are identified. Among these four nuclides with Z=llO, the alpha decay chains 0f’~~110, 26g110 and 273110 have been known since 1995 [1,4,5] and also studied theoretically [lo]. The experimental result on the alpha decay chain of 271110 has been formally published very recently [9,2] although the experiment was finished a few years ago. It is known from the experiment that the chain of 271110is a complete series of alpha decays to the known nuclides 255No and 251Fm [9,2]. As far as we know, there is no theoretical calculation on this chain of alpha decays [9,2] up to now. In this paper we report a deformed relativistic mean-field (RMF) calculation on the chain of 271110. This is also a further investigation of superheavy nuclei[lO,ll]. Before we calculate the properties of nuclei on the alpha decay chain of 271110 we test the RMF model with TMA force for known Cf and Fm nuclei at first. ’ 2. NUMERICAL

RESULTS

AND

DISCUSSIONS

The numerical results of Cf and Fm nuclei are listed in Table 1 where the deformed RMF codes in harmonic oscillator bases [12,10] are used. The force parameters TMA [lo] are inputted and the number of bases is chosen to be Nf = Nb = 20. The inputs of pairing *This work is supported by the National Natural Science Foundation 10125521, by the fund of Education Ministry of China under contract State Basic Research Development Program in China under contract knowledge Innovation Project No. KJCXS-SW-NOP. 0375-9474/03/$

- see front

doi:lO.l016/S0375-9474(03)01424-6

matter

0 2003 Published

by Elsevier

Science

No. No.

B.V

of China under 20010284036, G2000077400,

contract No. by the Major by the CAS

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gaps are A, = aP = 11.2/a MeV. An axial deformation is assumed in calculations. For the details of calculations please see the relevant publications [12,10]. In Table 1, B(the.) and B(exp.) are the theoretical binding energy and experimental one. The symbols ,& and & in Table 1 denote the quadrupole deformations of neutrons and protons, respectively. Further, the symbols Qa(the.) and Qcy(ezp.) are used for the calculated alpha-decay energies and experimental ones. Z’,(the.) and T,(ezp,.) are the theoretical half-life and experimental one where the theoretical one T,(the.) is calculated according to the Viola-Seaborg formula on alpha-decays [13,14]. This is a well-known formula and it is often used to estimate the half-life of alpha-decays by the decay energies [13,14]. It is seen clearly from Table 1 that theoretical binding energies agree well with the data. The theoretical decay energies are also close to experimental ones. N=172 could be a subshell or magic number for Cf and Fm isotopes due to its small alpha decay energy. This shows that RMF model is reliable for heavy nuclei. We have also used the force NLZ2 to calculate the properties of Cf and Fm nuclei. The results with NLZ2 are very close to those with TMA. Therefore we do not present the results with NL-Z2 here. After we test the model for Cf and Fm isotopes, we calculate the properties of nuclei on alpha decay chain of 271110. In numerical calculations of the ground state properties the blocking effect of odd neutron is omitted [lo] because our purpose is to discuss the alpha decay properties and binding energies. The contribution of the blocking effect on the total binding energy is very small and it does not alter the conclusion of this paper. The alpha decays occur from an odd-N nucleus to another odd-N nucleus and therefore the net effect of the blocking effect on the decay energies can be cancelled each other [lo]. This approximation is widely used for calculations of alpha decay energies [lO,ll]. Usually the blocking effect on alpha decays of heavy nuclei is mainly on the probability of the alpha particles or alpha clusters in the range of nuclear surface [15-171. This is the most important thing from the blocking effect but its treatment is beyond the current mean-field model and the other similar model such as the Moeller-Nix model [14]. Although this effect is not included for the calculations of the ground state properties, it is approximately included for the calculation of the lifetime. For the theoretical lifetime of the alpha decay, the blocking effect of odd neutron is included by using the famous Viola-Seaborg formula [13,14]. The numerical results are given in Tables 2 and 3. It is seen from Table 2 that the theoretical binding energies are very close to the experimental data for 255N~ and 251Fm. The average difference between the theoretical binding energy and experimental one is approximately 2 MeV. This corresponds to a relative difference 0.1%. The RMF model works well for the binding energy of the superheavy nuclei studied here. The theoretical alpha decay energies agree well with the experimental ones within 1 MeV. This ensures the good predicting ability of the RMF model for the alpha decay properties. The theoretical lifetime is close to the data. It is known from the binding energy formula that the alpha decay energies will vary smoothly with nucleon number if there is no shell effect or sub-shell effect. However there will be a sudden increase of alpha decay energies when there is a shell or a sub-shell [8,14,5]. There is a sudden increase of the experimental alpha decay energy when the proton number varies from Z=108 to 110 in Table 2. This corresponds to the possible closure Z=108 of the deformed shell effect. The RMF model can reproduce it to some extent. Calculations show

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Physics A722 (2003) 543c-547~

Table 1 The ground state properties of even-even Cf Nuclei B(MeV) /3n ,L$ Qa T, 242CE 1818.9 0.25 0.26 6.64 1.50 0.26 0.26 6.40 1.97 244Cf 1832.9 246Cf 1846.3 0.26 0.27 6.24 1.18 0.26 0.26 6.26 9.31 218Cf 1859.0 250(--f 1871.0 0.26 0.26 5.73 5.77 =%f 1882.4 0.25 0.26 5.34 1.11 254Cf 1892.9 0.25 0.25 5.55 6.12 256Cf 1903.0 0.23 0.23 5.36 8.80 2Wf 1912.9 0.22 0.22 5.02 1.33 26OCf 1922.7 0.21 0.21 4.70 2.88 0.20 0.19 4.60 1.79 Z6ZCf 1932.2 264Cf 1941.5 0.15 0.14 4.39 8.51 266Cf 1950.7 0.11 0.10 4.09 4.09 0.10 0.09 3.98 3.91 268Cf 1960.0 27OCf 1968.8 0.09 0.08 4.02 1.76 272Cf 1977.0 0.08 0.07 4.13 1.60 274Cf 1985.1 0.06 0.06 4.12 2.02 276Cf 1992.7 0.05 0.05 4.18 6.22 278Cf 2000.2 0.03 0.03 4.24 1.77 28OCf 2007.4 0.00 0.00 4.09 3.67 246Fm 1839.1 0.25 0.26 8.07 2.36 “48Fm 1853.4 0.26 0.27 7.80 2.02 0.26 0.27 7.61 1.03 “50Fm 1867.0 252Fm 1880.0 0.26 0.26 7.20 4.10 “54Fm 1892.5 0.26 0.26 6.80 2.05 256Fm 1903.7 0.25 0.26 7.00 2.74 “‘Frn 1914.5 0.25 0.25 6.77 2.93 0.21 0.21 6.22 1.28 260Fm 1925.0 262Fm 1935.5 0.21 0.21 5.75 3.95 264Fm 1945.5 0.20 0.20 5.51 1.06 266Fm 1955.2 0.17 0.16 5.28 2.87 “‘Frn 1964.6 0.14 0.14 5.15 2.32 270Fm 1974.2 0.11 0.11 4.82 4.75 272Fm 1983.4 0.10 0.10 4.86 2.28 274Fm 1992.1 0.09 0.09 5.00 2.55 276Fm 2000.4 0.07 0.07 4.98 3.21 278Fm 2008.4 0.06 0.06 4.98 3.48 “‘Frn 2016.1 0.04 0.04 5.00 2.47

and Fm even-even B(exp.1 x 106s 1817.3 x 107s 1831.3 1844.8 x 10’s x 107s 1857.8 x 1olOs 1870.0 x 1o=s 1881.3 x 10”s 1892.1 x 1012s x lOl5s x lOl7s x lol*s x lOl9s x 1022s x 1023s x 10z3s x 1022s x 1022s x lO=s x 1021s x 10z2s x lO1s 1837.2 x 102s 1851.6 x 103s 1865.5 x 104s 1878.9 x 106s 1891.0 x 105s 1902.5 x 106s x logs x lofis x 1013s x 101”s x 101”s x 1o17s x 1017s x 101”s x 1016s x 101”s x 1016s

nuclei

with

Qdev.1 7.52 7.33 6.86 6.36 6.13 6.22 5.93

8.37 8.00 7.56 7.15 7.31 7.03

TMA. Tdexp.) 2.09 x 1.16 x 1.29 x 2.88 x 4.12 x 8.34 x

102s 103s 105s 107s 108s 107s

3.60 1.80 9.14 1.17

10’s 103s 104s 104s

x x x x

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Z. Ren et al. /Nuclear Physics A722 (2003) 543c-547~

Table 2 The ground state properties of nuclei on the alpha decay chain 271110.The used in RMF calculations. Nuclei B (the.) (MeV) pn Pp Q,(the.) T,(the.) Qa(ew) 1.57 ms 275112 1985.58 0.20 0.20 11.36 271110 1968.64 0.21 0.22 11.18 1.07 ms 10.75 4.58 s 9.88 267HS 1951.52 0.23 0.23 9.54 Z63Sg 1932.76 0.26 0.27 9.27 5.94 s 9.26 141.1 s 8.88 25gRf 1913.73 0.26 0.27 8.60 255No 1894.03 0.26 0.27 7.85 9626 s 7.93 251Fm 1873.58 0.26 0.27 7.43 5.9 x 10” s The last two columns are experimental decay energies and lifetimes. The binding energies of 255N~ and 251Fm are known to be 1891.54 MeV and respectively [IS].

TMA

force is

T,(ew) 0.62 ms 74 ms 117 ms 1.72 s 37 s experimental 1871.69 MeV,

that there is a prolate deformation in the ground state of these nuclei. This agrees well with the calculation by Moeller et al [14]. For nuclei 259Rf and 255N~, a similar increase of alpha decay energies is observed and it could be associated with the deformed subshell N=152 [2,8]. It is seen from Table 1 that the theoretical lifetime is close to experimental value. The biggest difference on the lifetime is approximately 3 x lo2 times for 255N~. We would like to stress that it is very difficult to give an accurate value for lifetime by theories. The nuclear lifetime in nuclear charts is between infinite value and a very small value near zero. Usually the difference between theory and experirnent could be as large as 105. This is because the lifetime is very sensitive to the nuclear structure effect and the alpha decay energy. A small difference between the theoretical alpha decay energy and experimental value will lead to a very large difIerence of the lifetime. Table 3 is the RMF results with NLZ2 force. It is seen again that the theoretical results agree well with the experimental data of the binding energies and alpha decay energies. The precision of the force NLZ2 is as good as the force TMA. A quadrupole deformation in the ground state of these nuclei is also obtained for NLZ2. Its value is close to that of TMA force. This indicates that the RMF model is stable in this mass range. All previous discussions on Table 2 hold true for Table 3, When we compare Table 2 and Table 3 together, we notice the experimental binding energy is between the theoretical value with TMA and that with NLZ2. This is very useful for the prediction of binding energies of superheavy nuclei because both obtained values with TMA and NLZ2 are very close. In view of the fact that the nuclear binding energy is an important input to calculate the production cross-section of superheavy nuclei, the conclusion here is interesting for a good estimate of the unknown binding energy and for the production cross section of superheavy nuclei. 3. SUMMARY In summary the structure of the nuclei on the alpha decay chain of 271110 is investigated in the deformed RMF model. This is the first mean-field calculation on these new data from GSI [9,2]. The calculated binding energy agrees well with the available data. The

Z. Ren et al. /Nuclear Table 3 The ground state properties is used in RMF calculations. Nuclei B (the.) (MeV) 275112 1983.09 27’110 1966.21 267H~ 1948.53 1930.37 Z63Sg 259Rf 1911.22 255N~ 1890.61 1869.96 251Fm The last two columns are binding energies of 255N~ respectively [18].

of nuclei

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Physics A722 (2003) 543c-547~

on the alpha decay chain

27’110.

The NLZ2

force

pn Pp Q;jtt;.) T&he.) Qa(ew) Tdezp.1 1.14 ms 0.24 0.24 24.3 ms 10.75 0.62 ms 0.26 0.26 10.62 74 ms 0.28 0.29 10.14 99.6 ms 9.88 0.29 0.30 9.15 13.6 ms 9.26 117 ms 0.30 0.31 7.69 2.4 x lo5 s 8.88 1.72 s 7.65 5.4 x 10” s 7.93 37.0 s 0.30 0.31 0.31 0.31 7.75 3661.6s experimental decay energies and lifetimes. The experimental and 251Fm are known to be 1891.54 MeV and 1871.69 MeV,

calculations show that there are prolate deformations in these nuclei. This agrees with the experimental facts that there may be a prolate deformation around Z=108. The RMF results are in good agreement with the experimental data on the alpha decay energies and the lifetimes of the superheavy nuclei. The properties of 275112 are predicted and may be useful for future experiments on it. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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