Gareev F. A.

Kalinkin B. N.

Kalinkin B. N., Gareev F. A.

English

Samara University

ON THE PROBLEM OF SYNTHEZIS OF SUPERHEAVY NUCLEI.A SHORT HISTORICAL REVIEW ON FIRST THEORETICAL PREDICTIONS AND NEW EXPERIMENTAL REALITY.B.N. Kaiinkin and F.A. GareevIn connection with successful synthesis o f a superheavy nucleus with charge Z = 114 and mass number A = 288, 289 performed in Dubna [1] (see review paper [2]) it makes sense to recall theoretical studies in which for the .first time it has been predicted.The problem is closely related to the experimental fact: nuclei with Z = 8,20 ,28 ,50 ,82  (for neutrons also N = 126 ) are most stable to different decay modes. This phenomenon can be inter­preted in the framework o f the shell model [3] according to which the “magic” occupation numbers are those of one-particle levels in nuclei after which a considerable energy gap arises in the spec­trum, and the binding energy gets maximal. Consequently, a theoretical prediction o f the existence o f superheavy nuclei beyond the periodic table should at least be based on calculations o f one- particle proton and neutron spectra aimed at finding noticeable energy gaps in them.To the mid sixties when this problem arose, it became clear that the widely used oscillator potential (the Nilsson scheme) is not valid for that purpose. Perhaps, the only merit o f it is that the wave functions o f one-particle states are rather simple. Physically, its essential drawback is that the potential approaches to infinity near the surface of a nucleus. As a result, the wave functions of one- particle spectrum exhibit a wrong behavior on the surface and periphery of a nucleus, i.e. in the re­gion that essentially contributes to the probabilities of radiative transitions (the transition operator r % ( 0 , (p) , X = 1,2,3,...), elastic and inelastic scattering and to those o f other reactions. Thesecomputations are by an order o f magnitude larger or smaller than computations based on “correct’' wave functions. A serious drawback o f  that scheme is a necessary change o f parameters o f the po­tential and spin-orbital interaction when passing to a higher shell. Therefore, no wonder that com­putations o f the spectrum o f heavy nuclei based on the extrapolation o f those parameters to remote distances produced different magic values for Z and N . For example, Nilsson et all [4] obtained Z = 126 and N = 164, 184 . Obviously a scheme of that sort cannot be considered reliable, espe­cially, for predictions.A reasonable solution of the problem may be based on a realistic finite diffuse potential VN(r) as a mean nuclear field and on the justified form of the spin-orbital interaction [6,7]:-  -  1 dVvVs0 = k ( 1  ■ S) — L, (1)r drand also with the charge distributed over a nucleus. The most apt form of that potentialr - RVN(r) = - V 0/ .  ^  x\->1 + exp -  , R (1= r 0A 1/3, (2)к V a J)  was proposed by Saxon and Woods [8].In paper [9] (Kaiinkin B.N., Grabovskii Ya., Gareev F.A. “On levels o f  mean fie ld  o f  nu­c le i”, JINR preprint P-2682, 1966, the paper was submitted to publication in Acta Physica Polo- nica on April 6, 1966 and accepted on May 23, 1966) we employed just this potential with parame­ters V0, r0, а, к  fixed from the data on low-lying levels o f near-magic nuclei, on reactions o f one- nucleon transfers, elastic, inelastic scattering, and on polarization effects [10-13] . We developed an original method for numerical solution o f the Schroedinger equation with that potential and demon­strated its high accuracy.On June 16, 1966 we submitted for publication as a JINR preprint P-2793, 1966 and an arti­cle in the Phys.Lett. [5]: A. Sobiczewski, F.A. Gareev, B.N. Kaiinkin, “Closed shells fo r  Z > 82 and  N > 126 in a diffuse potential w ell”, Phys. Lett. V.22, No 4(1966)500, received 22 July 1966, pub­lished 1 September 1966.236In this paper, based on the method elaborated in [9], we calculated the proton and neutron energy levels versus A for Z > 82 and N > 126 for the Saxon-Woods potential with spin-orbital interaction. The results show that possible magic numbers are Z = 114 and N — 184 The computa­tions were carried out with the parameters taken from ref. [8]. The solution turned out to be stable to variations o f the parameters o f the potential and spin-orbital interaction caused by a possible inaccu­racy in their definition. No energy gap was observed in the system o f levels around Z  = 126.This paper has been the first publication in the available journals giving a clear statement on possible existence o f a superheavy nucleus with Z = 114; it presents both the method o f  solution and demonstrates the stability o f the latter within the framework o f a realistic potential with justi­fied values o f parameters.The importance o f use of justified values o f parameters for VN(r) and Vs0(r)  obtainedfrom the analysis of the data on low-lying levels of near-magic nuclei, on reactions o f one-nucleon transfers, elastic, inelastic scattering, and on polarization effects f 10-13] demonstrated by the results o f [14]. The parameter a in the potential VN(r) [14] has been used unjustified large magnitude (see for details [14]) which changed strongly spectrum of nuclei and lead to the magic number Z = 126.The JINR preprint P-2793 was then distributed by N.I. Pyatov among participants o f the Int. Symposium on Why and how should we investigate NUCLIDES FAR FROM THE STABILITY LINE, Lysekil, Sweden, August 21-27, 1966, where the considered problem was o f  common inter­est (Session IX: Nucleosynthesis; Chairman: W.J. Swiatecki).In the report [15] by H. Meldner: "Predictions o f  new magic regions and masses fo r  super­heavy nuclei from  calculations with realistic shell model single particle hamiltonians ”, Proc. o f  the Intern. Lyseki Symposium, Sweden, August 21-27, 1966. Received 14 September 1966, published  18 October 1967, Ark. Fys. 36(1967)593.H. Meldner informed that new magic numbers should be Z  = 114 and N = 184 and at the end made the comment: ‘‘Note added in p ro o f In the meantime the proton shell Z  = 114 has been fo und  in independent investigations [1 3 ]”. Reference [13] o f that report is [13] Nilsson S.G., pri­vate communications, Strutinsky V.M., private communications, Sobiczewski A., Gareev F.A., Ka- linkin B.N. (preprint).So, when H. Meldner submitted his report on September 14, 1966, he already had our pre­print. We consider also that our studies and studies by H. Meldner were carried out independently. However, we do not agree with G. Herrmann, the author of recent paper [16], from which it may be concluded that it was just H. Meldner who first predicted magic numbers Z  = 114 and N = 184 Let us discuss this question in greater detail.In [15], p. 595, H. Meldner reported:The same result was obtained in simpler calculations with local potentials two years ago [9] (in [9] see discussion on superheavy nuclei in W.D. Myers and W.J Swiatecki, Nucl. Phys. 81,1 (1966); or UCRL-11980(1965), based on calculations quoted there under ref. [23]).In paper by W.D. Myers and W.J. Swiatecki, Nucl. Phys. 81,1 (1966), ref. [23] looks as fol­lows:[23] H. Meldner and P. Roper (Institut fu r  Theoretische Physik der Universitat Frank­furt/M.), personal communication (1965).We quote a brief fragment from that paper (pp. 49, 50 ): “In our mass form ula we have in­cluded, fo r  purposes o f  illustration, magic numbers at Z = 126 and  N = 184, 258, see f ig  19. ( the latter numbers are obtained by follow ing the sequence o f  major shells in harmonic oscillator poten­tial with spin-orbit coupling). We do not wish to imply that there are grounds fo r  believing that any o f  these magic numbers would show up in practice, and we use them only to illustrate that some o f  the consequences would be i f  a magic number turned out to be present in the general neighborhood o f  superheavy nuclei somewhat beyond the end o f  the periodic table. The actual values o f  the magic numbers might be different; fo r  example, we have recently learned [23] that Z  = 114 N = 184 is a237possible candidate fo r  a doubly magic nucleus... What we wish to point out is that i f  a (double) magic number exists, then an important consideration affecting the possible stability o f  the corre­sponding nucleus is the considerable increase in the barrier against fission and, consequently, in the spontaneous fission half-life.. . . In order to proceed in a realistic manner with discussion o f  the existence and location of possible islands o f  stability beyond the periodic table the first requirement is the availability o f  es­timates fo r  the location and strength o f  rnagic number effects in that region. When such estimates have become available (through single-particle calculations in realistic nuclear potentials) it will be possible to apply our semi-empirical treatment o f  nuclear masses and deformations to the pre­dictions o f  the fission barriers o f  hypothetical superheavy nuclei... ”From the above quotations it follows that:•  First, W.D. Myers and W.J. Swiatecki in their calculations used the values o f magic num ­bers obtained by other authors with the use o f harmonic potential. Estimates on the basis o f realistic potentials were not available for them at that time.• Second, they obtained information on a possible realization of the double magic nucleus with Z  = 114, N = 184 from a personal communication of H. Meldner and P. Roper who did not published them anywhere, which is verified by the absence o f any reference to that work in the re­port [15].It is obvious that personal communications cannot be reason o f the priority. The priority re­quires official publications o f results with the method they have been obtained, accuracy, and stabil­ity o f the solution permitting verification o f the results by any physicistIt remains to declare that the report by H, Meldner [15] is his first official communication on possible existence o f the nucleus with Z = 114.The following two reports are also devoted to realization o f superheavy nuclei.In the report [17]:C. Gustafson, I.L. Lamm, B. Nilsson, S.G. Nilsson, “Nuclear deformations in the rare-earth and actinide regions with excursions o f f  the stability line and into the superheavy elements ”, Re­ceived 14 September 1966, published in Ark. Fys. 36(1967)613 it is stated that as a by-product o f  these computations it appears reasonable to forecast that the “mastic” proton candidate is Z  = 114 and not Z  = 126 while for neutrons N = 184 is a rather questionable “m agic” number. These pre­dictions remain valid also when a reasonable extrapolation is made in the values ц and t  (Fig. 5,cf. ref. [81) [8] Sobiczewski, Gareev and Kalinkin, to appear in Nucl. Phys.In the report [18]:V.M. Strutinsky, ‘‘Microscopic calculations o f  the nucleon shell effects in the deformation energy of nuclei”, received 14 September 1966, published in Ark. Fys. 36(1967)629.The behavior o f deformation energy is studied for some heavy and superheavy nuclei with consideration for shell effects. Use is made for the “Nilsson scheme” (a traditional version). T he most stable nucleus has been that with 126310. Possible realization of a nucleus with Z  = 114 is not discussed.Next “burst” o f the activity in discussing the existence of superheavy nuclei took place at the International conference on the physics o f heavy nuclei held at Dubna on October 13-19, 1966. There two reports were delivered [19,20]:V.M. Strutinskii and Yu. A. Muzychka “Some shell effects in transuranium nuclei ”,A.M. Friedman, “Calculations on the production o f  the next closed shell nucleus and other nuclei”.Based on a realistic potential, the authors conclude that Z  = 114 and N = 184 are the most pronounced magic numbers in the region o f superheavy nuclei. Also, both the reports do not refer to our work [5]. Proceedings o f that conference were published on October 16, 1967.Concluding a brief review of studies made in 1966 and devoted to the possibility o f exis­tence o f a heavy nucleus with Z  = 114, we note once more that it has first been predicted in our work [5].238It is also important to recall that our method of solving the problem [5] was later verified by V.A. Chepurnov [21] who reproduced our results by direct numerical solution with a high accuracy. Also, we generalized it to a realistic nuclear field for strongly deformed nuclei [22-29]. Practical application o f the generalized method in a lot o f investigations on the spectroscopy o f the rare-earth and transuranium group carried out at the BLTP, JINR in recent years (see, e.g., monographs [30,31]) has proved its high efficiency. Therefore, we may hope, it could be used for studying su­perheavy deformed nuclei o f the island of stability whose actual synthesis begins just now.Evidence for the island of stability to exist rather than a single superheavy nucleus, to our mind, comes from the logic of [5] the very fact o f synthesis o f the nucleus with the magic number o f protons Z = 114 and nonmagic number o f neutrons N = 175. If so, then stable should be both the doubly magic nucleus with Z  = 114 and N = 184 (the island center) and the nucleus with the nonmagic number o f protons Z = 114 and magic number o f neutrons N = 184 . Nuclei with Z and N near the above-mentioned combinations should also be stable [32].So, the theoretical prediction of a superheavy nucleus with Z  = 114, formulated for the first time at Dubna [5], that has allowed a goal-directed experimental search has been testified by its ac­tual synthesis also at Dubna many years later.In conclusion, we note that the synthesis o f superheavy nucleus 289 114 was further devel­oped: new heaviest nuclides 288114 and 284112 were observed [34]. An attempt o f synthesis o f the superheavy nuclei was performed in Berkeley [33]. This attempt was commented in [34]:“The synthesis o f  293 118 and its sequential a-particle emission to the daughter isotopes with Z = 116 -106 in the bombardment o f  208 Pb with 2.3 -1018 449-MeV 86 K r ions using the Berkeley separator BGS was announced in April-May, 1999. Three decay chains were observed, each consisting o f  an implanted atom and six subsequent a  -decays. Another experiment with this reaction was carried out at the same bombarding energy at GSI, in Darmstadt, using the separator SHIP. No correlated a -decay chains were observed yet, with a similar beam dose o f  2.9 • 1018 K r ions [35]”. Therefore, the results o f analyzing this reaction is to be continued.Thus, the experimental research o f the island o f stability for superheavy nuclei was started with a high activity.References1. O ganessian Yu. Ts. et al., Preprint JINR E-7-99-53, Dubna, 1999; JAF, V63, 1769, 2000; Phys. Rev., C 62.0411604(R ), 2000; Phys. Rev. Lett., 83. 3154, 1999; N ature (London) 400, 242, 1999; Eur. Phys. J. A5, 63, 1999; Oganessian Yu. Ts., JAF 63. 1391, 2000.2. H ofm ann S., M unzenberg G., Reviews o f  M odern Physics, 72, 733, 2000.3. Preston M .A., Physics o f  N ucleons. Addison-W 'eslag Pub. C., Jnc., Reading, M assachusetts, Palo-Alto-London, 1962.4. N ilsson S.G., Kgl Danske Vidensk, Selsk. mat-fys. Medd. 22, N 16 (1955); M ottelson B .R , N ilsson S.G., Kgl Dan- ske Vidensk, Selsk. mat-fys. kr. 1, N 8 (1959).5. Gareev F.A., Kaiinkin B.N., Sobiczewski A., JINR P-2793, 1966; Phys. Lett. 22 (1966)500.6. D avydov A.S., Teoriya atom nogo yadra. Fiz.-mat. GIZ, M oskow, 1958.7. H eizenberg W., Teorie des A tomkerns, Gottingen, 1951.8. Saxon D , W oods R„ Phys. Rev. 95(1954)577.9. Kaiinkin B.N., Grabovskii Ya., Gareev F.A., J INR P-2682, 1966; Acta Physica Polonica, XXX, N6(1966)999.10. Elton L.R.B., N uclear sizes. Oxford University Press, 1961.11. Hodgson P.E., The optical model o f  elastic scattering. Oxford, The Clarendon Press, 1963.12. Levintov I .I ,  Physica XXII (1956)1178; JETP, 30(1958)987.13. N em irovskii P .E , Sovrem ennye modeli atom nogo yadra. A tomizdat, M oscow, 1960.14. W o n g C .Y , Phys. Lett. 21(1966)688.15. M eldner H ,  Proc. o f  the Intern. Lysekil Symposium, Sweden, Aug. 21-27, 1966. Received 14 Septem ber 1966, published 18 Oct. 1967, Ark. 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Bang J., Gareev F.A., Pusynin I.V., Jam alejev R.M ., N uclear Physics A261(1976)59.25. Bang J., G areev F.A., Ivanova S.P., Particles and Nuclei 9(1978)286.26. G areev F.A., C hem ei M.I., Ivanova S.P., Soviet Journal o f  N uclear Physics 9(1969)308.27. G areev F.A., K alinkin B.N., Pyatov N.I., Chem ei M .I., Soviet Journal o f  N uclear Physics 8(1968)305.28. Shulz H „ W iebicke H.J., G areev F.A., Nucl. Phys. A180( 1972)625.29. G areev F.A., Ivanova S.P., M alov L.A., Soloviev V.G., Nucl. Phys. A171(1971)3.30. Soloviev V.G., T eoriya sloznyh yader. Nauka, M oscow, 1971.31. Soloviev V.G., T eoriya sloznyh yader. Yadernye modeli. Energoizdat, Moscow, 1981.32. K alinkin B.N., Gareev F.A., Preprint JINR E7-99-107, D ubr 1999.33. N inov V. et al„ Phys. Rev. Lett. 83(1999)1104.34. Oganessian Yu. Ts. et al., Preprint JINR E-7-99-347, Dubna, 1999;35. Hofman S. et al., private comm unication.240

On the problem of synthczis of superheavy nuclei. A short historical review on first theoretical predictions and new experimental reality

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On the problem of synthczis of superheavy nuclei. A short historical review on first theoretical predictions and new experimental reality

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