Explore the in-depth analysis of beta-decay, neutron emission, and ground state properties in heavy isotopes like K, Ca, and Sc. This study covers theoretical models, density functional theory, self-consistent approaches, and comparisons of global models to understand nuclear properties. Discover the latest research insights in particle physics and astrophysics from leading institutions in Moscow and Dubna, Russia.
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IAEA REFERENCE DATABASE FOR BETA-DELAYED NEUTRON EMISSION EVALUATION I.N.Borzov National Research Centre Kurchatov Institute , Moscow, Russia Bogolubov Laboratory of Theoretical Physics Joint Institute of Nuclear Research, Dubna, Russia DELAYED MULTI-NEUTRON EMISSION IN HEAVY K, C , Sc ISOTOPES The 3rd international conference on particle physics and astrophysics 2 5 October 2017, Moscow, Russia
Beta-decay studies of Why Ca region is interesting for K , Ca , Sc isotopes at N>28 theory and RIBs exp.? Magic shells N=20, 28 and new sell- closures at N=32,34. D. Steppenbeck et al., Nature Physics (2013) G.s. spin inversion at N>28. K. Krein et al. Phys. Letts. B73, 97 (2013) (47 -51K). K , Ca , Sc isotopes Exp. on optical isotope shifts. Huge <r2>1/2charge at N=32 52Ca (r2) 48,52= 0.530 fm2 Garcia-Ruiz et al., Nature (2016) (52Ca) CERN : K isotopes
Outline : Self-consistent approach to beta-decay. Density functional theory is the method of choice. Comparing performance of the recent GLOBAL MODELS : (Parameters fitted to few sample nuclei stay the same for all A .) DF + Continuum QRPA DF3- spherical ~300 quasi-spherical nuclei; I.N.B. PRC 67, 025802 (2003) Relativistic HB + QRPA D3C*- spherical all nuclei; T. Marketin et al. Phys. Rev. C 93, 025805 (2016). Finite Amplitude Method Sk(yrme) O - deformed all even-even nuclei T. Mustonen, J. Engel et al. PR C90, 024308 (2014); odd for A=80, 160 DF : Quality of the ground state description: cf. quasi-particle energies and Q , Sxn values and the J/ of the ground state. QRPA: Reliability of strength functions cf. available decay schemes and integral quantities. Effects beyond the QRPA: 2nd-QRPA with Quasiparticle-Phonon Coupling (QPC) and Shell-Model
Self Self- -Consistent Ground State Consistent Ground State An upper limit of exact E total: p Tr = h 2 = = H + [ , ] [ , ] E E h int 2 M 2 p E = = + + h ~ = * , 1 Kohn Sham quasiparticle local EDF M m 2 1 2 E = + [ ] int [ ] * E F = = int n iterative , , main Coul sl volume HFB like procedure h + F surface , , , , h 0 0 0 0 1 1 1 1 DF3 functional by S. Fayans et al. DF3 I.N. Borzov, S.A. Fayans, E. Kromer, D. Zawischa Z. Phys. A335(1996) 117 S.A. Fayans, S.V. Tolokonnikov,E.Trykov, D. Zawischa, Nucl.Phys. A676 (2000) 49. FaNDF0 S.A. Fayans JETP Letters 68,169 (1998)
Self-Consistent Ground State . Fayans EDF. Fayans EDF DF Skyrme EDF Sk At = 0 DF - dependence is similar to Skyrme ansatz . DF vs Sk Effective mass = bare mass (m* /MN = 1) Sophisticated density dependence of int : linear-fractional (Pade-like) structure Pairing DF depends on the gradient of density NB ! Y.S. Lutostansky, E.E. Saperstein. J. Phys. G 42, 076102 (2015) NB ! Proposal of hybrid functional normal part of Sk + pairing part of DF : P.-G. Reinhard, W. Nazarewicz. nucl-th 1704.07430 (2017) Deformed DF S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen,
Potassium isotopes. DF3 beta decay energy release and x-neutron emission window (Q xn) . 24 | Q th - exp| is less than 500 KeV ; 22 Q Q exp Q est # Q n Q n exp Q 2n Q 2n exp 20 Q , Q xn, MeV For A=54,55 our DF3 calculation gives (about 2 MeV) higher Q , Q n , Q 2n values cf. to the estimated (!) in AME-2016 18 16 14 12 10 8 These isotopes are rather far from neutron drip-line. DF3 d.l. @ 64K, 68Ca, 70Sc 6 4 K isotopes 2 0 44 46 48 50 52 54 56 A How theory describes the exp. data on Q n , T1/2 and Pn tot in the inversion region and at N=32, 34 shell-closures? In 47-56K chain 1n 4n emission possible! How the Pn tot is distributed between 1n - 4n phase-subspaces
Ground state spin inversion in K isotopes. Phys.Rev.C90 , 034321 (2014) DF3 has a provision to fix g.s. J/ What is an impact on the beta decay properties ? ISOLDE Proposal IS599 K isotopes : Towards A=54
Spin-isospin excitations (GT, FF). Continuum pn-QRPA based on the Fayans energy-density functional S=0, T=1 (nn,pp) mass dependent g.s . paring + S=1, T=0 (pn) dynamic pairing Continuum pnQRPA, full ph-basis, SO(8) symmetry TATTA=1T=1 g/s/ paring and T= /s/ pairing M ller, P.; Nix, J. R.; Kratz, K.-L. ADNDT, Vol. 66, p.131,1996 Pairing only in the g.s. Dynamic pairing ignored. BCS + RPA, SU(4) . Spurious effects. Particle-hole channel: -interaction with Landau-Migdal constant g + -meson + -meson exchange U: V: Particle-particle channel: T=0, -interaction with one parameter: g pp CQRPA : are taken the same for all nuclei with A>40. NN-interaction parameters (ph):
Delayed multi-neutron emission probability : beta decay strength function + xn-phase-spaces ??? = ?1/2? 1?? 2 ? ? (?+1)?? ?0(? + 1 ,?) ?? ?? ,? ) ??????? ????(?,? ?? ? (??) 6 B(GT)m 0 2 4 8 10 *(MeV) ????:???????????? 18 m Az + E1 16 x3/2 Q 5n Q 4n 14 S5n 12 10 Q S4n ? ?0(? + 1 ,?) ~ ? 8 Q 3n Q 2n 60Ca 6 S3n 4 S2n ? ???????? ???????? ? ????(?,? S1n Q 1n 2 Az+1 ?? ?? ,? ) Two main beta decay channels : Gamow-Teller (GT) and first-forbidden (FF). NB! Balance of the GT and FF decays. Key structural indicator is FF % = FF / tot !
Half-lives. Total Pn values. DF3 T1/2 stabilization near g.s.spin re-inversion at A=51. Strong shell effects (T1/2 drops) at N=32+1n , 34+1n. Exp. and DF3 half-lives mirror one another at A=50,51 and N=32,33. DF3 Pn increases near spin inversion (N=47-49) and re-inversion (at A=51) regions. DF3 cf. RHB Strong odd-even effect in RHB High Pn values at N=32+n , 34+n. Both in DF3 and RHB for A=48-56 % FF is small: about of 10-14% ! What is the reason for T1/2 decrease at A=54?
Gamow-Teller strength functions of 53,54K Reduction of the T1/2(A) at A=54 is not due to opening of the FF transitions , as it happens at crossings of the major neutron shells N =50, 82. In Ca region near N=34, it is due to the low-Ex GT state! 54K W 1,2 1,0 B(GT) 53 K S_GT 0,8 0,6 Ca ground state Q =19.299 MeV Qbn 0,4 0,2 Ex 0,0 2 4 6 8 10 12 14 16 18 20 22 24 54Ca 0,6 B(GT) S_GT 54 K 54K: N=34+1n Strong GT transition is opened: 0,4 Q =21.499 MeV 0n 0,2 1n 4n 3n 2n DF3+CQRPA: | 1f5/2- p1f7/2 > Ex=6.4 MeV Just 200KeV below Qbn (beyond S2n) 0,0 0 2 4 6 8 10 12 14 16 18 20 22 24 W, MeV Qbxn, MeV P2n prediction is very sensitive to the strength near the 2n-threshold !
High delayed 2-neutron emission in 53-56 K 100 80 DF3 P tot P1n P2n P3n 60 Pxn, % RHB 40 P2n EXP P tot 20 0 50 52 54 56 58 A For more realistic estimate we would have included some surface effect : - Coupling of the low-lying GT excitations with the surface phonons ( 2+ ) ; ( Simple account for GT spreading width results in ~20% Lower P2n. ) One may even think of neutron skin or even 2n-halo effects... - Cross section for Coulomb dissociation in 2n channel (?) - Di-neutron decay to deutron. Search for beta-delayed deutron emission !
See also in K. Minamisono et.al. Phys.Rev. Lett. (2017) DF3-a + A-fluctuating part of L / = 2+, 3- phonons The Ca-anomaly at N= 30-34 is explained by A-fluctuating part of QPC ! A correlation of <r2> ch and Rnp with P2n !
Mass dependence of K isotopes radii N=34 Formation of neutron skin . N=32 A kink shows some speeding up near the new subshells N=32,34. Volume pairing old exp new exp surf + grad surf vol Anomalously high charge radii in K and Ca isotopes at N>28 3,55 Rch, fm 3,50 Impact of pairing correlations on rms charged radii 3,45 K isotopes Volume pairing; Surface paring; Gradient pairing. 35 40 45 50 55 Mass number A
CONCLUSIONS Integral characteristics {T1/2, Pxn} constrain the -strength functions due to correlation of the half-lives and P(x)n-values. G.S. spin-inversion in 50 - 51K stabilizes their half-lives. T1/2 speeds up at N=34+1n due to appearance of the low-lying GT state. Minor influence of FF decay @ N~32-34, clean GT case. QPC is a basic mechanism needed to make realistic estimates of the P2n and <r2>ch. orrelations between high P(x)n, neutron skin Rnp , and anomalous <r2>ch gives a possibility to constrain the QPC-coupling strength.
Acknowledgments N.A. Arsenyev, A.P. Severyukhin, E.V. Sushenok, V .V. Voronov BLTP, JINR, Dubna Yu.S. Lutostansky, E.E. Saperstein, S.V. Tolokonnikov NRC Kurchatov Institute , Moscow N. Van Giai, J. Margeuron, D. Verney IPN, Orsay R. Grzywacz, K. Rykaczewski UTK, Knoxville, ORNL, Oak Ridge
Adequate description of the phase-space(s) is important . Q , Sxn are treated on equal footing with (q-p). 11 18 10 Q MeV 9 Q eV 16 8 14 7 12 6 FAM DF3a AME 2012 5 10 Exp DF3a FAM 4 8 3 Sn Ni 6 2 1 4 70 72 74 76 78 80 82 84 86 88 132 134 136 A 138 140 A Reference chains : Ni, Sn DF3 | Q | is up to 600 KeV , FAM underestimates Q up to 1.5 MeV, RHB ? Underestimation of the Q may cause distortion of the -decay half-lives, Pn values I.N.B. Phys.Rev. C 67 025802 (2003); Phys. At. Nucl. 79 (6) 921 (2016).
RIKEN: EURICA and BRIKEN CAMPAIGNS (N~34,50, 82) 2012 -2016: 440 isotopes! 2017 Expected: 200 more isotopes! Also studies at Z ~20, N>28 , especially near new sub-shells N=32,34 CERN - ORNL, JINR-ORSAY (~34) , RIKEN (~34, 50,82)
The IAEA support of participation in the CRP Development of a Reference Database for Beta-Delayed Neutron Emission is acknowledged. The study is partially supported by the Russian Scientific Foundation Physical Review Letters 117, 012501 (2016) First applications of the Fayans functional to deformed nuclei S V Tolokonnikov1,2, I N Borzov1,3, M Kortelainen4,5, Yu S Lutostansky1 and E E Saperstein1,6 Journal of Physics G: Nuclear and Particle Physics, Volume 42, Number 7 , p 075102 (2015) I.N. Borzov1,2 Self-consistent approach to beta decay and delayed neutron emission Physics of Atomic Nuclei, Volume 79, Issue 6, pp 910 923 (2016) DELAYED MULTI-NEUTRON EMISSION IN NEUTRON-RICH CA REGION In Proc. VIII Int.Symposium EXON-2016, 4 -10 Sept. 2016, Kazan, RF. Physics of Atomic Nuclei 2017, (submitted) A. P. Severyukhin,1,2 N. N. Arsenyev,1 I. N. Borzov,3,1 and E. O. Sushenok1,2 Multi-neutron emission of Cd isotopes PHYSICAL REVIEW C 95, 034314 (2017)
