Hayakawa, T

Kajino, T

Nakada, H

Ogawa, K

Shizuma, T

CERN Document Server

PoS(NIC-IX)112Cosmic clock and thermometer for neutrino processT.Hayakawa∗ †, T.ShizumaKansai Photon Science Institute, Japan Atomic Energy Agency, Kizu, Kyoto 619-0215, Japan.E-mail: hayakawa.takehito@jaea.go.jpT.KajinoNational Astronomical Observatory, Osawa, Mitaka, Tokyo 181-8588, Japan.K.Ogawa, H.NakadaChiba University, Inage, Chiba 263-8522, Japan.We suggest a 138La - 138Ce - 136Ce system as a new nuclear cosmic clock for measuring the timeelapsed from a single neutrino process episode to the present. This clock is applied to meteoriticsamples produced mainly by a single nucleosynthesis episode. The nuclear structure of 138Lais crucial for the performance of this clock and its astrophysical origin. The lowest 1+ state in138La has not been established experimentally. If this state is a β unstable isomer, 138La shouldbe destroyed in the ν-process and the clock cannot work well. However, this system can be usedas a new cosmic thermometer. To study the nuclear structure of 138La, we perform a shell modelcalculation. Our shell model calculation shows the 1+ state may be stable against the β decayand our proposed clock can perform.International Symposium on Nuclear Astrophysics — Nuclei in the Cosmos — IXJune 25-30 2006CERN, Geneva, Switzerland∗Speaker.†This work has been supported in part by Grants-in-Aid for Scientific Research (18340071).c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)112Cosmic clock and thermometer for ν-process T.Hayakawa135Ba 136Ba 137Ba 138Ba138La 139La2nd p 1st p 141Pr134Ba140Ce138Ce136Ceγ processNeutral current reactionCharged current reactionν processβ- decaysA pair of two p nucleiFigure 1: A partial nuclear chart around La and nucleosynthesis processes.1. IntroductionLong-lived radioactivities are used as the cosmic clocks but only six clocks with their half-lives of 1 ∼ 100 Gyr are known. They are 40K [1], 87Rb [2] and 176Lu [3, 4] for the s-processor explosive nucleosynthesis in supernovae (SNe), and 187Re [2, 5, 6], 232Th [1] and 238U [1] forthe r-process. However, the long-lived cosmic clock for the neutrino reaction nucleosynthesis insupernovae (ν-process) has not been proposed.The ν-process was proposed as origin of some rare isotopes of heavy elements and light ele-ments [7]. An isotope 138La is a key to understand the ν-process [7, 8, 9, 10, 11, 12] because onlytwo isotopes, 138La and 180Ta, among the heavy elements are considered to be mainly synthesizedby the ν-process [7, 9] but 180Ta is also considered to be produced by the s process [13] or the p-process (γ-process) [14]. A contribution of a charged current reaction to 138La was quantitativelycalculated [8]. Recently, a result that about 90% in the solar abundance of 138La can be explainedby the ν-process was reported [9]. However, the origin of 138La has not been established by as-tronomical observations or analyses of meteorites. We propose a new nuclear cosmic clock forthe nucleosynthesis process of 138La and to present a shell model calculation result of the nuclearstructure of 138La, which is of importance to the performance of the clock.2. Proposal of a new cosmic clock for the ν-processThe nucleus 138La decays to 138Ce or 138Ba with a half-life of 10.1× 1010 yr. Here we suggesta 138La - 138Ce - 136Ce system as a new cosmic clock for the ν-process. This clock is applied tometeoritic samples whose compositions were mainly produced by a single nucleosynthesis episode.The pre-existing p-nuclei including the three nuclei almost disappear by the weak s-process in anevolutionary state of massive stars. The three nuclei are synthesized in different layers in the SNexplosion. The meteoritic compositions are produced after the mixing of the materials originatedfrom the different layers. Thus a single meteoritic sample may include the three isotopes. Since themanner of the mixing in individual meteorites is different, the estimation of the initial abundanceof 138Ce is difficult.In our proposed system the initial γ-process abundance of 138Ce can be calculated by an em-pirical scaling law between two p-nuclei with the same atomic number, which was found in thesolar system abundances [4]. There are nine such pairs in nature. As shown in Fig. 1, the first and2PoS(NIC-IX)112Cosmic clock and thermometer for ν-process T.Hayakawa5+1+138Ba138La0+138Ba(υe,e-)138La   reaction0+0+Excited states138Ce 136CeIntermediate statesLowest 1+ stateγ processEC decayLow spinβ− decayν processPhoton excitationsNuclear thermometerGround stateT1/2=101 GyrFigure 2: A schematic view for the synthesis and destroy of 138La in the ν-processsecond p-nuclei are lighter than the s-nucleus by two and four neutrons, respectively. We foundthe empirical scaling law that the abundance ratios of N(1st p)/N(2nd p) is almost constant in awide region of atomic number, where N is the solar abundance [4]. This empirical law leads to "theuniversality of the γ-process" that the scaling holds for nuclei produced in individual SNe [4, 15].If the abundances of 136,138Ce and 138La in a single sample produced mainly by a single su-pernova are measured, the time elapsed from a ν-process episode, T , can be calculated byT =−T1/2(138La)ln2 ×ln(N(138La)N(138La)+ 1b(N(138Ce)−Rpp(Ce)×N(136Ce)) ), (2.1)where N is the observed abundance in the sample, Rpp is the initial N(1st p)/N(2nd p) ratio atthe freezeout of the γ-process, and b is the branching ratio of the β− decay of 138La: λ (β−) /(λ (β−)+λ (EC)). The Rpp(Ce) ratio can be estimated by γ-process theoretical calculations or theempirical scaling [4, 15]. The isotopic fractions of two elements of La and Ti in individual Al-Ca-rich inclusions were measured [16]. Recent studies of the meteorites show that we can expect thatthe samples of which 138La is enhanced will be found.3. Effect of the nuclear structure of 138LaThe nuclear structure of 138La is crucial for its nucleosynthesis and the performance of ourproposed clock. The nucleus 138La (N=81) is lighter than 140Pr (N=81) by two protons and thesetwo nuclei locate near a neutron magic number of N=82. A fact that the ground state of 140Pr isJpi=1+ suggests that the 1+ state may exist at a low excitation energy in 138La. The lowest 1+ statein 138La has not been established experimentally. If the 1+ state appear at low excitation energy,it may be a β unstable isomer since β decay from the 1+ state can compete with an internal E4transition to the 5+ ground state. Our proposed clock cannot work well since the synthesized 138Lais destroyed via the β -decay of the 1+ isomer populated by (γ ,γ’) reactions through intermediatestates, but this system can be used as a cosmic thermometer like the 176Lu thermometer [17].3PoS(NIC-IX)112Cosmic clock and thermometer for ν-process T.HayakawaWe calculate the nuclear structure of 138La and 140Pr in a shell-model. In a mass region around138La, the last proton can occupy either d5/2 or g7/2 orbit around the Fermi surface. The last neu-tron can occupy the d3/2 orbit: namely, a hole of d3/2 of a N=82 magic core. The 1+ and 5+ statesin these nuclei can be understood by (pid5/2)⊗(νd3/2)−1 and (pig7/2)⊗(νd3/2)−1 configurations, re-spectively. We would like to stress that the observed 1+ ground state of 140Pr can not be understoodby a simple shell-model picture because a coupling between a proton particle and a neutron holecannot lead to the ground state with Jpi=1+ [18].In our calculation, we take all orbits in the Z,N = 50− 82 major shell, restricting excitationfrom (pig7/2d5/2) to (pih11/2s1/2d3/2) up to 3 protons, and the proton seniority to v≤ 3. The effec-tive Hamiltonian has the following form,H = Hpi +Hν +Vpiν ;Hpi =∑jε(pi)j ˆN(pi)j +Vpipi , Hν =∑jε(ν)j ˆN(ν)j , (3.1)where ˆN(pi)j ( ˆN(ν)j ) represents the proton (neutron-hole) number operator on the orbit j. A surface-delta form (Yukawa form) is adopted for the proton-proton interaction Vpipi (the proton-neutroninteraction Vpiν ). The single-particle energies ε(pi,ν)j are determined from low-lying energy levels ofneighboring N = 81,82 nuclei. As shown in Fig. 3, we successfully describe the observed excitedstates [19] lower than 500 keV and, in particular, the ground state spin of 140Pr. We find that thecoupling of two- and four-particle excited configurations of pi(g7/2)−2(d5/2)3 and pi(g7/2)−4(d5/2)5leads to the 1+ ground state.Next, we apply this shell-model calculation to 138La. As shown in Fig. 3, the calculated levelsare consistent with the observed ones [20, 18]. It is noted that the 1+ state locates at a low excitationenergy as low as 169 keV. This energy is lower than the previously calculated energy ∼ 250 keV[18] because we use the extended interactions and larger space. This result suggests that the lowest1+ state may be stable against the β decay.4. SummaryWe suggest a 138La - 138Ce - 136Ce system as a new nuclear cosmic clock for measuring thepassing time from a single ν-process episode. This clock is used in analyses of primitive meteorites,which compositions were mainly produced by a single supernova. A 1+ state should exist at a lowexcitation energy in 138La. If the 1+ state is an isomer, our proposed clock does not work well. Westudy the nuclear structure of 138La and 140Pr in shell model calcualtions. We reproduce the groundstate of 140Pr state including a coupling of two and four particle excitation states from g7/2 to d5/2.The calculated result shows that the 1+ state in 138La may be stable against the β decay.References[1] E.M. Burbidge, G.R. Burbidge, W.A. Fowler, F. Hoyle, Rev. Mod. Phys. 29, 548 (1957).[2] D.D. Clayton, Astrophys. J. 139, 637 (1964).[3] J. Audouze, W.A. Fowler, D.N. Schramm, Nature Phys. Sci. 238, 8 (1972).4PoS(NIC-IX)112Cosmic clock and thermometer for ν-process T.Hayakawa27127  0 291271921+3+2+(5  )+3+2+  06076912051682+3+3+5+2+1+ 5+(3)+3+5+(2)+2+(2)+3+(3)+2+(4)+4+1+0100200250115160191231 227169155107 947259  0   0140Pr 138LaCalculationExperiment 50150CalculationExperiment3004+ 350350400(4)+ 4144503733+4174+2873+3314+390(4   )+290+4Figure 3: Calculated and observed level schemes of 138La and 140Pr.[4] T. Hayakawa et al., Phys. Rev. Lett. 93, 161102 (2004).[5] T. Hayakawa et al., Astrophys. J. 628, 533 (2005).[6] T. Hayakawa et al., Phys. Rev. C 74, 065802 (2006).[7] S.E. Woosley, D.H. Hartmann, R.D. Hoffman and W.C. Haxton, Astrophys. J. 356, 272 (1990).[8] S. Goriely, M. Arnould, I. Borzov, M. Rayet, Astron. Astrophys. 375, L35 (2001).[9] A. Heger et al., Phys. Lett. B 606, 258 (2005).[10] T. Yoshida, T. Kajino, D.H. Hartmann, Phys. Rev. Lett. 94, 231101 (2005).[11] J. Pruet, R.D. Hoffman, S.E. Woosley, H.-T. Janka, R. Buras, Astrophys. J. 644, 1028 (2006).[12] C. Fröhlich, et al., Phys. Rev. Lett. 96, 142502 (2006).[13] K. Yokoi and K. Takahashi, Nature 305, 198-201 (1983).[14] M. Rayet et al., Astron. Astrophys. 298, 517 (1995).[15] T. Hayakawa et al., Astrophys. J. 648, L47 (2006).[16] J.J. Shen and T. Lee, Astrophys. J. 596, L109 (2003).[17] H. Beer, F. Käppeler, K. Wisshak and R.A. Ward, Astrophys. J., 46, 295 (1981).[18] V.D. Helton, J.C. Hiebert and J.B. Ball, Nucl. Phys. A 201, 225 (1973).[19] S.G. Hussein, N.E.Sanderson, R.G.Summers-Gill, Nucl. Phys. A 219, 407 (1974).[20] R.D. Lasijo, K. Sheline, R.D. Griffioen and J.L. DuBard, Nucl. Phys. A, 253, 17 (1972).5

Cosmic clock and thermometer for neutrino process

Abstract

Similar works

Full text

Available Versions

CERN Document Server