Superheavy nuclei are investigated in a nonlinear chiral SU(3)-model. The proton number Z=120 and neutron numbers of N=172, 184 and 198 are predicted to be magic. The charge distributions and alpha-decay chains hint towards a hollow stucture

Beckmann, Christian

Greiner, Walter

Papazoglou, Panajotis

Schramm, Stefan

Stöcker, Horst

Zschiesche, Detlef

English

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/0002046 v1   18 Feb 2000Superheavy Nuclei in a Chiral Hadronic ModelCh. Beckmann, P. Papazoglou, D. ZschiescheS. Schramm, H. St¨ ocker, W. GreinerInstitut f¨ ur Theoretische PhysikJohann Wolfgang Goethe Universit¨ at, D-60054 Frankfurt am MainAbstractSuperheavy nuclei are investigated in a nonlinear chiral SU(3)-model. Theproton number Z=120 and neutron numbers of N=172, 184 and 198 are pre-dicted to be magic. The charge distributions and α-decay chains hint towardsa hollow stucture.Reasonable descriptions of nuclei directly derived from QCD models are still not in sight.However, one can investigate eﬀective models that incorporate basic symmetries of QCD,describing hadronic properties as well as nuclear matter and ﬁnite nuclei [1,2]. The approachdiscussed here [2] builds on chiral SU(3)L ×SU(3)R symmetry and broken scale-invariance.The model incorporates relativistic baryonic and mesonic degrees of freedom (nucleons,hyperons, spin 32 baryons, the spin-0 and spin-1 SU(3)-multiplets [2]). The hadron massesare generated dynamically via spontaneous symmetry breaking. The masses of the nucleonsare generated by the interactions with a non-strange scalar ﬁeld σ ∼  uu+dd  and a strangecondensate ζ ∼  ss  asmN = gNσσ + gNζζ. (1)Other baryonic masses are generated in the same manner. The pseudoscalar mesons obtaintheir masses by explicit symmetry breaking.Our present investigation of superheavy nuclei uses three diﬀerent sets of parameters. Thecalculations are performed in spherical symmetry adopting the mean-ﬁeld approximation.Free parameters are ﬁxed to vacuum properties of hadrons and ground state properties ofinﬁnite nuclear matter (Set C1) and via a χ2-ﬁt to properties of the spherical nuclei 16O,40Ca, 48Ca, 58Ni, 90Zr, 112Sn, 124Sn and 208Pb (Set C1ﬁt).The χ2-function is given byχ2 =Xn Oexpn − Otheon∆On!2, (2)where Oexpn is the experimental value of the observable On, while Otheon is its calculatedvalue. ∆On is a weight given by the experimental error. However, because all observablesare known experimentally to much better accuracy than provided by the model, we havedecided to use the weights to make the ﬁts comparable to other calculations. The observ-ables used for the ﬁts to the nuclei are the binding energy EB, the surface thickness σ and1the charge diﬀraction radius Rdiﬀ. For extrapolation to heavy nuclei one should replace 16Oby 264Hs as done in the parameter set C1hs. All parameter sets give reasonable results inthe region of known nuclei. This is a remarkable result particularly for the ﬁt to hadronproperties and nuclear matter (C1), which does not contain any information about ﬁnitenuclei. The ﬁt to ﬁnite nuclei can be used to improve the χ2. All parameter sets give thecorrect shell closures for magic nuclei up to 82 protons and 126 neutrons.Several experiments have recently attempted to produce nuclei with proton numbers beyondthe element Z = 112 that was found at GSI [4]. Experiments report observation of the nu-cleus 293118175 [3]. Also Z = 114 has been reported [5].The most important theoretical question is where new shell closures are to be expected.These nuclei could have very long lifetimes (minutes to years). This topic has been ex-tensively investigated in Walecka type models [6] predicting Z = 114 and Z=120 as nextshell closure. Let us now turn to the predictions of the chiral model. Figure 1 shows theﬁnite-nucleus calculation (in the chiral model) of the two-proton gapδ2p(Z,N) = S2p(Z,N) − S2p(Z + 2,N) (3)with the 2p-separation energy S2p deﬁned asS2p(Z,N) = EB(Z − 2,N) − EB(Z,N) (4)The calculation was done for a nucleus with N = 172. The signature for a shell closure is apronounced peak in the two-nucleon gap. One can see that all three parameter sets show ashell closure at Z = 120. At Z = 114 a small peak is also visible. It is interesting to see thatthe weak peak at Z = 114 is suppressed, if the parameter set includes the binding energyof 265Hs (C1hs), thus taking into account a known heavy nucleus in the vicinity of Z ∼114. This seems to suggest that Z = 114 is not a magic number (C1hs should give the bestprediction for superheavy nuclei). This result has recently also been obtained in Walecka-type models – the early famous Z=114 predictions are attributed to an incorrect spin-orbitforce in nonrelativistic models [6]. The two-nucleon separation energy (4) shows that for aneutron number N = 172 the nucleus with Z = 120 is beyond the dripline (S2p < 0) inthe calculation with the ”nuclear matter” ﬁt parameters C1 (Figure 2). However for theparameter sets C1ﬁt and C1hs (adjusted to properties of ﬁnite nuclei) 292120 is a bounddoubly magic nucleus, clearly above the dripline. And for 184 neutrons, Z = 120 yieldsS2p > 0 for all three parameter sets. N = 172, 184 and 198 are closed neutron shells. Figure3 shows the predicted α particle decay chain of the nucleus Z = 120 and N = 172. Theα energy decreases slightly towards the lighter daughter nuclei and drops to about 4 Mevfor Z = 106. This overall trend is in qualitative agreement with the experimental ﬁndingof nearly constant α-energies for Z=118, N=175 [3]. One should keep in mind that thiscalculations are performed under the assumption of spherical symmetry which is probablynot fulﬁlled for this nuclei, except Z = 120 which shall be magic.The predicted charge distribution of 292120 is shown in ﬁgure 4. Note its strong depletion inthe center of the nucleus. The same eﬀect is seen in Walecka model calculations [7]. Henceone may speculate that the superheavy nuclei around Z=120 exhibit a Fullerene, bucky-ballstructure built of 60 α-particles and ≈ 60 neutrons (See ﬁgure 5). The length of the linksbetween the α-particles in a Fulleren-type structure for Z=120 (radius 8.0 fm) is about 3.5fm. This is surprisingly close to twice the radius of 4He (Rdiﬀ = 1.68 fm). Such a structurenaturally exhibits a depleted charge density in the center of the nucleus.2ACKNOWLEDGMENTSThis work was supported by GSI, BMBF, DFG and the Josef Buchmann Stiftung. Wethank Henning Weber for his help with ﬁgure 5.3REFERENCES[1] E. K. Heide, S. Rudaz, P. J. Ellis, Nucl. Phys. A571 (1994) 713[2] P. Papazoglou, D. Zschiesche, S. Schramm, J. Schaﬀner-Bielich, H. St¨ ocker, W. Greiner,Phys. Rev. C59 411[3] V. Ninov et al., to be published[4] S. Hofmann, V. Ninov, F. P. Hessberger, P. Armbruster, H. Folger, G. M¨ unzenberg, H. J.Sch¨ ott, A. G. Popeko, A. V. Yeremin, S. Saro, R. Janik, M. Leino, Z. Phys. A354 (1996)229[5] Y. Oganessian et al., to be published[6] K. Rutz, M. Bender, T. B¨ urvenich, T. Schilling, P.-G. Reinhard, J. A. Maruhn, W.Greiner, Phys. Rev. C56 (1997) 238[7] M. Bender, K. Rutz, P.-G. Reinhard, J. A. Maruhn, W. Greiner, to be published in Phys.Rev. C4FIGURES110 112 114 116 118 120 122 124Z1.01.52.02.53.03.54.02pC1hsC1ﬁtC1FIG. 1. Two-Proton Gap110 112 114 116 118 120 122 124Z-6-4-2024681012S2pC1hsC1ﬁtC1FIG. 2. Two Proton Separation Energy S2p for N=1725106 108 110 112 114 116 118 120Z23456789101112E[MeV]FIG. 3. Predicted Alpha Decay Energy for Superheavy Nuclei as a Function of Charge0 2 4 6 8 10 12r [fm]0.00.010.020.030.040.050.060.07ChargeDensity[e/fm3]C1FITC1292120FIG. 4. Charge Density Distribution of Z = 120, N = 1726FIG. 5. Alpha-Cluster with 60 α-Particles7

Superheavy nuclei in a chiral hadronic model

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main