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IDIIOCHIDINO$ $1,11DPI.I!MIiNT$ Nuclear PhysicsB (Proc. Suppl.) 112 (2002) 30-35
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NEUTRINO-NUCLEUS REACTIONS IN SUPERNOVAE K. Langanke a G. Mart~nez-Pinedo b aInstitute for Physics and Astronomy, University of Aarhus, Aarhus, Denmark bDepartement fiir Physik und Astronomie der Universit~it Basel, Basel, Schweiz
Neutrino-nucleus reactions in the supernova environment occur on the MeV and tens of MeV energy scale. At these energies the processes are dominated by allowed and first-forbidden transitions and are quite sensitive to the proper description of nuclear structure. Significant progress in shell-model computing, mainly achieved by the Strassbourg-Madrid collaboration [1] and in particular due to Etienne Caurier, allows now to reliably describe the Gamow-Teller (GT) response of medium-mass nuclei. This is the dominant excitation mode for electron captures during the presupernova evolution. It also constitutes an important example to illustrate the importance of a proper description of the microphysics in a supernova collapse, as we will briefly show below. GT transitions also dominate neutrino-nucleus reactions for neutrino energies less than ,,, 15 MeV; at higher energies forbidden transitions, mainly dipole and spin-dipole responses, become relevant as well. These are usually dominated by the collective response to the giant resonances so that a model like the random phase approximation (RPA) is usually sufficient to describe the non-allowed contributions to the neutrino-nucleus cross sections. Such hybrid models (shell model for allowed and RPA for forbidden transitions) have recently been used to calculate neutrinonucleus cross sections under supernova conditions. A detailed description of the current corecollapse supernova picture is given in [2]. Neutrinos in general and neutrino-nucleus reactions in particular play an important role in the latestage evolution of massive stars and their subset
quent core collapse, leading to a type II supernova event. During the collapse phase, neutrinos are mainly produced by electron captures on nuclei (and in the late stage also on free protons). This process is made possible by the increasing density in the star's center, which, accompanied by an increase of the chemical potential (Fermi energy) of the degenerate electron gas, enables electrons to be captured by nuclei. This process sets in for densities > 10° g/cm 3 (which are achieved during oxygen burning) and is a very efficient cooling mechanism for the star, as the produced neutrinos can leave the star unhindered at such densities. Electron captures reduce the electron-to-baryon ratio Ye of the matter composition which has two important consequences for the subsequent evolution. 1) The electron pressure which acts against the gravitational contraction is reduced. This, together with the energy losses by neutrino emission, accelerates the collapse. 2) In the late stage evolution (following silicon core burning) the temperature in the core is sufficiently high (a few 100 keV) to keep reactions mediated by the strong and electromagnetic (but not the weak) interaction in equilibrium; the matter composition is then in nuclear statistical equlibrium and a decrease of Ye makes the matter composition more neutronrich. The relevant captures occur on nuclei in the iron mass range which, during silicon burning, become abundant in the core. The respective stellar weak-interaction rates have been recently evaluated [3,4] on the basis of large-scale shell model calculations [5], supplemented by experimental data whereever available. The shell model
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K. Langanke, G. Martinez-Pinedo /Nuclear Physics B (Proc. Suppl.) 112 (2002) 30-35
electron capture rates turned out to be systematically and significantly smaller than the previous estimates based on the independent particle model and the data then available [6]. This difference leads to noticeable changes in the presupernova evolution of massive stars (until the central density reaches about 101° g/cm3), which are examplified in Fig. 1 in terms of the three decisive quantities for the collapse: i) the central electronto-baryon ratio Ye increases with the new rates. This suggests a larger homologous core size after neutrino trapping; ii) the iron core masses are reduced. Together with i) this implies that the shock wave has less material to traverse reducing its energy losses; iii) for stars with M < 20Mo the entropy is smaller. As a consequence, the abundance of free protons is smaller. We remark that the conclusions drawn above have yet to be confirmed in simulations of the subsequent collapse and bounce phase. As we will see below, this phase requires, additional to the changes in the initial presupernova models, also updates in the considered microphysics. Details of the presupernova studies with the shell model weakinteraction rates can be found in [7,8]. We note that these studies also show that beta-decays, an additional source for stellar cooling, become competative during a short period in silicon burning. As electron captures drive the matter more neutronrich, the matter composition in the collapse phase, post the presupernova models, will be dominated by nuclei with neutron numbers N > 40 and proton numbers Z < 40. In the simple independent particle model, which is employed to estimate the electron capture rates in the collapse phase, GT transitions are then completely Pauli-blocked. As a consequence electron capture on nuclei ceases out in these simulations [9,10]. However, the Pauli blocking of the GT transitions will be overcome by thermal excitations [11] and correlation effects [12]. It appears that electron capture on nuclei can compete with capture on free protons (see Fig. 2) also in the later stage of the collapse, if these effects are taken into account. Neutrino interactions with matter cannot longer be ignored if the density exceeds about 101° g/cm 3. Elastic neutrino scattering off nu-
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Figure 1. Comparison of the center values of Ye (left), the iron core sizes (middle) and the central entropy (right) for 11 - 4 0 M o stars for presupernova models based on the weak-interaction rates derived from the independent particle model (WW) and from the shell model (LMP) [7].
clei and inelastic scattering on electrons are the two most important neutrino-induced reactions during the collapse. The first reaction randomizes the neutrino paths out of the core and, at densities of a few 1011 g/cm 3, the neutrino diffusion time-scale gets larger than the collapse time; the neutrinos are trapped in the core for the rest of the contraction. Inelastic scattering off electrons thermalizes the trapped neutrinos then rather fastly with the matter and the core collapses as a homologous unit until it reaches densities slightly in excess of nuclear matter, generating a bounce and launching a shock wave which traverses through the infaUing material on top of the homologous core. In the currently favored explosion model, the shock wave is not energetic enough to explode the star, it gets stalled before reaching the outer edge of the iron core, but is then eventually revived due to energy transfer by neutrinos from the cooling remnant in the center to the matter behind the stalled shock. It has been suggested that inelastic neutrino scattering on nuclei might be important during the infall phase [10] and that 'preheating' by neutrinoinduced neutral- and charged-current reactions can help to revive the stalled shock [14]. However, none of these processes are currently considered
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,,t.-,tU~ Figure 2. Comparison of electron capture rates for selected nuclei with neutron number N > 40 and for free protons as function of the electron chemical potential covering the range from the presupernova models at densities p ,~ 10 l° g/cm s to the phase of neutrino thermalization at p ,,, 1012 g/cm 3. No Pauli blocking in the final state has been considered. In NSE the abundance ratio of free protons to heavy nuclei increases from < 0.01 to ,~ 0.1 during this infall epoch. (from [13])
in supernova simulations, as the required cross sections were not available. This has changed recently. We note that during the collapse only ~e neutrinos are present. Thus, charged-current reactions A (re, e-)A' are strongly blocked by the large electron chemical potential [10,15]. Inelastic neutrino scattering on nuclei can compete with (re,e-) scattering at higher neutrino energies E~ > 20 MeV [10]. Here the cross sections are mainly dominated by first-forbidden transitions. Finiteterhperature effects play an important role for inelastic v + A scattering below EVI_< 10 MeV. This comes about as nuclear states get thermally excited which are .connected to the ground state and low,lying excited, states by modestly strong GT transitions and increased phase space. As a consequence the cross sections are significantly increased for low neutrino energies at finite temperature and might be comparable to inelastic
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Figure 3. Cross sections for inelastic neutrino scattering on nuclei at finite temperature. The temperatures are given in MeV [16]
~e + e- scattering [16]. Examples are shown in Fig. 3. Finite temperature effects become unimportant for stellar inelastic neutrino-nucleus cross sections once the neutrino energy is large enough to reach the GTo centroid, i.e. for E~ _> 10 MeV. Besides electron neutrinos produced by electron captures the protoneutron star generates additionally neutrinos by the transformation of electron-positron pairs into uP pairs. This process generates pairs of all 3 neutrino flavors with the same luminosity and thus is the main mechanism for the production of v,, vT neutrinos and their antiparticles. These neutrinos can interact with the dense matter of the star only via neutralcurrent reactions and hence have smaller opacities than ve and Pe electrons which can also interact with neutrons and protons via the charged current. As a consequence, ~,,vr neutrinos have larger average energies (~ 25 MeV), when they leave the dense matter region, than Pe ( " 16 MeV) and ve (~ 11 MeV) neutrinos. The neutrino interactions in dense matter is paid currently a lot of attention. As the topic is somewhat outside of the scope touched upon in this contribution we refer only to the relevant literature: [17,18] and references therein. The region above the nascent protoneutron star
K. Langanke, G. Martinez-Pinedo/Nuclear Physics B (Proc. Suppl.) 112 (2002) 30-35
has been proposed as the possible site of the nuclear r-process (nentrino-driven wind model, [19,20]). The r-process forms approximately half of the heavy elements with mass number ,4 > 70 and all of the transuranics by a sequence of rapid neutron captures, interrupted by occasional /~decays [21]. If the neutrino-driven wind model is indeed the r-process site, the process occurs in strong neutrino fluxes and neutrino-nucleus reactions can have interesting effects. The most 'problematic' is the a-effect [22]. The matter leaving the neutron star surface are mainly free nucleons with an excess of neutrons over protons as Ye < 0.5 [23]. When the matter reaches cooler temperatures, nueleosynthesis starts and the free protons are assemblied into a-particles, with some extra neutrons remaining. These neutrons become the source for the r-process, once additional nucleosynthesis has transformed some of the a-particles into heavy nuclei, the r-process seed. However, the neutrons are still exposed to the large neutrino flux which will change some of the neutrons via ve + n --~ p + e- into protons, which, together with additional neutrons, are also bound into a-particles. Thus, the a-effect reduces severely the neutronto-seed ratio and is quite contraproductive to a successful r-process. A possible way out of the dilemma requires that the dynamical thnescale of the ejected matter is very short; i.e. the matter flies so fast away from the neutron star surface that neutrinos have not enough time to transform neutrons into protons. Such scenarios have been studied by Meyer et al. [22] and Terasawa [24], the later using the novel RPA neutrino-nucleus reaction cross sections of [25]. In the neutrino-driven wind model the rprocess is a dynamical process, in which the astrophysical time scale (passage time through the region with favorable r-process conditions) competes with the internal time scale of the process, which is mainly given by the sum of the various fLdecays. Here it is important to note that recent calculations indicate that the halflives of the r-process waiting point nuclei (the nuclei with the longest halilives along the r-process path associated with the magic neutron numbers N --- 50, 82 and 126) are significantly shorter than previously
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assumed ([26] and references therein). Due to the immense neutrino fluxes, (t/e, e-) reactions can compete with/~decays at rather modest distances above the neutron star and speedup the r-process matter-fl0w to heavier nuclei (see Fig. 4). We note, however, that the average energy of supernova z/e neutrinos is about 12 MeV. Thus, in contrast to/~-halflives, neutrino absorption on neutronrich nuclei can be rather accurately calculated as the capture is dominated by allowed transitions which are governed by sumrules. Capture to the low-energy tail of the GT_ distribution has been estimated to introduce an uncertainty of about a factor 2 into the cross sections [27]. We stress that absorption cross sections for supernova neutrinos do not pronounce magic neutron numbers [28]. Thus, the occurence of the peaks in the r-process elemental abundance distribution signals that at freeze-out /~-decays have to be faster than neutrino absorption [22]. This puts constraints on the neutrino flux at the time and position of the freeze-out. In both re-induced charged-current and v~,~induced neutral-current reactions the final nucleus will be in an excited state and most likely decays by the emission of one or several neutrons. If these processes occur after freeze-out the neutrons will not be recaptured and the r-process abundance is changed due to this neutrino postprocessing [30]. Neutrino postprocessing can be relevant for the peak distributions where it removes some abundance from the top of the peaks and shifts it to the wings at smaller mass numbers. Considering that the postprocessing contribution cannot be more than the observed abundance for the wing nuclides allows one to put constraints on the neutrino fluence in the neutrinodriven wind scenario [31].
Acknowledgement The work has been in part supported by the Danish Research Council. REFERENCES 1. A. Pores and F. Nowacki, Lecture Notes in Physics 581 (Springer-Veralg Berlin, 2001) p.
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70 2. H.A. Bethe, Rev. Mod. Phys. 62 (1990) 801 3. K. Langanke and G. Martinez-Pinedo, Nucl. Phys. A673 (2000) 481 4. K. Langanke and G. Martinez-Pinedo, At. Data Nucl. Data Tables 79 (2001) 1 5. E. Caurier, K. Langanke, G. Martinez-Pinedo and F. Nowacki, Nucl. Phys. A653 (1999) 439 6. G.M. Fuller, W.A. Fowler and M.J. Newman, ApJS 42 (1980) 447;48 (1982) 279; ApJ 252 (1982) 715 ;293 (1985) 1 7. A. Heger, K. Langanke, G. Martinez-Pinedo and S.E. Woosley, Phys. Rev. Lett. 86 (2001) 1678 8. A. Heger, S.E. Woosley, G. Martinez-Pinedo and K. Langanke, Ap.J. 560 (2001) 307 9. S.W. Bruenn, Ap.JS 58 (1985) 771 10. S.W. Bruenn and W.C. Haxton, ApJ. 376 (1991) 678 11. J. Cooperstein and J. Wambach, Nucl. Phys. A420 (1984) 591 12. K. Langanke, E. Kolbe and D.J. Dean, Phys. Rev. C63 (2001) 032801 13. J.M. Sampaio, K. Langanke, E. Kolbe, G. Martinez-Pinedo and D.J. Dean, to be published 14. W.C. Haxton, Phys. Rev. Lett. 60 (1988) 1999 15~ K. Langanke, G. Martinez-Pinedo and J.M. Sampaio, Phys. Rev. C64 (2001) 055801 16, J.M. Sampaio, K. Langanke, G . MartinezPinedo and D.J. Dean, Phys. Lett. B529 (2002) 19 17. A. Burrows and R.F. Sawyer, Phys. Rev. C58 (1998) 554 18. S. /teddy, M. Prakash, J.M. Lattimer and S.A. Pons, Phys. Rev C59 (1999) 2888 19. K. Takahashi, J. Witti and H.-T. Janka, Astron. Astrophys. 286 (1994) 857 20. S.E. Woosley e~ al., Ap.J. 433 (1994) 229 21. G.J. Mathews and J.J. Cowan, Nature 345 (1990) 491 and references therein 22. B.S. Meyer, G. McLanghlin and G.M. Fuller, Phys. Rev. C58 (1998) 3696 23. Y.-Z. Qian and G.M. Fuller, Phys. Rev. D52 (1995) 656 24. M. Terasawa, P h . D . thesis, University of Tokyo, (2002)
25. K. Langanke and E. Kolbe, At. Data Nucl. Data Tables, 79 (2001) 293 and in print 26. G. Martinez-Pinedo and K. Langanke, Phys. Rev. Lett. 83 (1999) 4502 27. R. Surman and J. Engel, Phys. Rev. C58 (1998) 2526 28. A. Hektor, E. Kolbe, K. Langanke and J. Toivanen, Phys. Rev. C61 (2000) 055803 29. G. Martinez-Pinedo, Nucl. Phys. A688 (2001) 357c 30. Y.-Z. Qian, W.C. Haxton, K. Langanke and P. Vogel, Phys. Rev. C55 (1997) 1532 31. W.C. Haxton, K. Langanke, Y.-Z. Qian and P. Vogel, Phys. Rev. Lett. 78 (1997) 2694
K. Langanke, G. Martinez-Pinedo ~Nuclear Physics B (Proc. Suppl.) 112 (2002) 30-35
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Figure 4. Halflives for (v~, e - ) absorption and 3decay on N = 50, 82 and 126 waiting point nuclei. The calculations have been performed assuming a Fermi-Dirac spectrum for the neutrinos with zero chemical potential and T = 4 MeV (describing superuova ve neutrinos) and T = 8 MeV (assuming complete ve ~ v~,~ oscillations). The luminosity was set to 1051 erg/s at a radius of 100 km [30]. The 3-decay halflives are from shell-model calculations [29].
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