Neutral-Current Neutrino-Nucleus Inelastic Reactions for Core Collapse Supernovae

Transcription

1 Neutral-Current Neutrno-Nucleus Inelastc Reactons for Core Collapse Supernovae A. Juodagalvs Teornės Fzkos r Astronomjos Insttutas, Lthuana E-mal: andrusj@tpa.lt J. M. Sampao Centro de Físca Nuclear da Unversdade de Lsboa, Portugal E-mal: sampao@c.fc.ul.pt K. Langanke Gesellschaft für Schweronenforschung (GSI), Germany G. Martínez-Pnedo Gesellschaft für Schweronenforschung (GSI), Germany W. R. Hx Physcs Dvson, Oak Rdge Natonal Laboratory (ORNL), USA H.-Th. Janka Max-Planck-Insttut für Astrophysk (MPA), Germany We study neutrno-nucleus nelastc reactons of pf-shell nucle for core-collapse supernovae. Cross-sectons are computed takng nto account detaled nuclear response and thermal exctaton of nuclear states. Internatonal Symposum on Nuclear Astrophyscs Nucle n the Cosmos IX June CERN, Geneva, Swtzerland Speaker. A footnote may follow. c Copyrght owned by the author(s) under the terms of the Creatve Commons Attrbuton-NonCommercal-ShareAlke Lcence.

2 Neutrno-nucleus nelastc reactons for SNe J. M. Sampao 1. Introducton Neutrno reactons are mportant n many astrophyscal scenaros. In supernova they play a fundamental role n the dynamcs of the collapse and evoluton of the post-bounce shock as well as n the followng explosve nucleosynthess. Durng the collapse phase, neutrnos are produced manly n electron captures and they escape the star s core carryng energy away. About 99% of the energy avalable from gravtatonal collapse s lost n the form of neutrnos. However, wth denstes n excess of ρ 1 g cm 3, neutrno nteractons wth matter become mportant n the tme-scale of the collapse and, eventually, equlbrum between neutrnos and matter s establshed - neutrno thermalzaton takes place (ρ 2 g cm 3 ). To date, collapse smulatons have consdered neutrno nelastc scatterng on electrons and free nucleons as the man mechansm for thermalzaton. However, n 1988, Haxton argued that the exctaton of the nuclear gant resonances n the supernova envronment can lead to sgnfcant cross-sectons of nelastc neutrno-nucleus reactons and these should, therefore, be added n supernova smulatons [1]. Moreover, recently mproved nuclear models have shown that electron capture rates on nucle domnate captures on free protons and suggested the same mght be the case for neutrno-nucleus reactons [2, 3]. The poneerng study of nelastc neutrno scatterng and absorpton reactons on nucle n supernova was done by Bruenn and Haxton [4]. In ther study, the nuclear composton was approxmated by a sngle nucleus - Fe - and the rates were calculated based on a nuclear model approprate for temperatures T = 0. They found that nelastc neutrno-nucleus scatterng plays an mportant role n equlbratng neutrnos wth matter. More recently, notceable fnte-temperature effects n the low-energy cross-sectons were found by Sampao et al., usng results from largescale Shell-Model calculatons of the allowed GT transtons [5, 6]. The study was performed on representatve nucle, suggestng nuclear structure effects on the fnte-temperature dependence of the cross-sectons. Followng up ths work, neutral-current neutrno-nucleus nelastc reactons were studed on a larger set of ron group nucle relevant n the supernova composton[10]. The cross-sectons were extended to hgher neutrno energes and forbdden transtons were added. Here, we recall the man results of ths study, but also new results of folded cross-sectons over the nuclear composton are shown for relevant stellar condtons. 2. Model To descrbe the neutral-current neutrno-nucleus nelastc reacton, we splt the cross-secton nto two components: σ ν = σ SM ν + σ RPA ν (2.1) where σ SM ν descrbes the (allowed) neutral Gamow-Teller, GT 0, contrbutons, derved from largescale Shell-Model (SM) dagonalzaton of pf-shell nucle [7]; and σ RPA ν descrbes the hgher multpole (forbdden) transtons, derved from the Random Phase Approxmaton (RPA) [8]. The SM component accounts for detaled nuclear structure, correlatons and fnte-temperature effects, whch are mportant for low-energy neutrno scatterng (E ν 15 MeV). To derve t, we use the same procedure as n [5, 6]: The SM component s splt nto one term descrbng neutrno 2

3 Neutrno-nucleus nelastc reactons for SNe J. M. Sampao σ ν (10-42 cm 2 ) Fe 53 Mn N Co SM (T=0.8 MeV) SM (T=1.2 MeV) SM (T=1.6 MeV) RPA Total Fgure 1: Neutral-current nelastc neutrno-nucleus cross-sectons for four selected nucle and three fntetemperatures. down-scatterng (E f ν < E ν), ndependent of temperature, and another term descrbng neutrno upscatterng (E f ν > E ν), whch depends on temperature. At hgh neutrno energes, scatterng s domnated by the bulk propertes (total strength and centrod) of the hgher multpole resonances, whch can be well descrbed by the RPA. Our RPA calculatons were done wthn the Independent Partcle Model occupaton number formalsm and, hence, ths component s ndependent of temperature. 3. Results and dscusson Fnte-temperature effects of low energy neutrno-nucleus cross-sectons are strongly dependent on the energy of the centrod of the GT 0 gant resonances (E x 10 MeV) and on the densty and relatve transton strengths of the low-lyng states. Cross-sectons for four selected nucle as a functon of the ntal neutrno energy are shown n Fg. 1 for three dfferent temperatures: T = 0.8 MeV ( K), T = 1.2 MeV ( K) and T = 1.6 MeV ( K). These temperatures roughly correspond to the presupernova, neutrno trappng and neutrno thermalzaton phases of the core-collapse supernova evoluton. Enhancement due to thermal exctaton s notable for E ν 10 MeV, especally n even-even nucle ( Fe) and some odd-a nucle wth a closed f 7/2 neutron orbt ( 53 Mn). These effects become neglgble once E ν s large enough to allow for transtons to the GT 0 centrod. For E ν MeV allowed and forbdden transtons contrbute about equally to the cross-secton, whle at E ν > 100 MeV, forbdden transtons domnate [10]. A new process that s possble when one consders thermal exctatons s neutrno up-scatterng (Eν f > Eν). Ths effect s best shown by fnal state neutrno energy dstrbutons. Fg. 2 shows the 3

4 Neutrno-nucleus nelastc reactons for SNe J. M. Sampao n (MeV -1 ) 53 Mn =30 MeV =10 MeV =6 MeV Co =30 MeV =10 MeV Eν =6 MeV T=0.8 MeV T=1.2 MeV T=1.6 MeV f Fgure 2: Normalzed fnal state neutrno spectra for two nucle and three ntal neutrno energes and three temperatures. normalzed fnal state neutrno spectra for two nucle and for three ntal neutrno energes. Upscatterng s notable for E ν = 6 MeV n 53 Mn. Lke n Fe these exctatons are mportant for nucle wth a small densty of low-lyng GT 0 states. Thermal exctatons are less mportant when neutrnos are down-scattered by low-lyng states, mally n odd-a and odd-odd nucle, here represented by Co and 59 N. At E ν = 30 MeV neutrnos are essentally down-scattered by the bulk of the GT resonances for all nucle. Supernova smulatons requre cross-sectons folded over the stellar nuclear composton, defned as: σ ν = ky k σ k ν k Y k (3.1) where Y k s the number abundance of the nucleus k for a gven densty (ρ), electron fracton (Y e ) and temperature (T ). Here we use abundances gven by the NSE Equaton of State [9]. Fg. 3 llustrates the folded cross-sectons over a pool of 52 ron group nucle for three temperatures and three denstes (ρy e ). Thermal enhancement of E ν < 5 MeV cross-sectons s notable over the nuclear pool. Above 15 MeV, cross-sectons can be parameterzed by scatterng from an average nucleus, chosen to approxmate the matter composton. Foldng of neutral-current neutrno-nucleus nelastc cross-sectons was done for a large number of stellar condtons and the results of the mpact n supernova smulatons are expected soon. 4

5 Neutrno-nucleus nelastc reactons for SNe J. M. Sampao Folded cross-sectons <σ ν > (10-42 cm 2 ) 10-4 T=0.8 MeV, ρy e =5x0 mol/cm 3 T=1.2 MeV T=1.6 MeV ρy e =5x1 mol/cm 3 ρy e =5x2 mol/cm Fgure 3: NSE-folded cross-sectons over a pool of 52 pf-shell nucle for three temperatures and three denstes. Densty-dependence s neglgble compared wth temperature-dependence of the cross-sectons. References [1] W. C. Haxton, Phys. Rev. Lett. 60 (1988) [2] K. Langanke et al., Phys. Rev. Lett. 90 (2003) [3] W. R. Hx et al., Phys. Rev. Lett. (2003). [4] S. Bruenn, W. C. Haxton, Astrophys. J. suppl. Ser. 58 (1991) 376. [5] J. M. Sampao et al., Phys. Lett. B 511 (2001) 11. [6] J. M. Sampao et al., Phys. Lett. B 529 (2002) 19. [7] K. Langanke and G. Martínez-Pnedo, Nucl. Phys. A 673 (2000) 481. [8] E. Kolbe et al.,nucl. Phys. A 540 (1992) 80. [9] W. R. Hx, prvate communcaton. [10] A. Juodagalvs et al., Nucl. Phys. A 747 (2005) 87. 5