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Formation of Hot Heavy Nuclei in Supernova Explosions Physics Letters B 584 (2004) 233–240 www.elsevier.com/locate/physletb Formation of hot heavy nuclei in supernova explosions A.S. Botvina a,b, I.N. Mishustin c,d,e a Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA b Institute for Nuclear Research, 117312 Moscow, Russia c Institut für Theoretische Physik, Goethe Universität, D-60054 Frankfurt am Main, Germany d Niels Bohr Institute, DK-2100 Copenhagen, Denmark e Kurchatov Institute, RRC, 123182 Moscow, Russia Received 30 December 2003; accepted 23 January 2004 Editor: P.V. Landshoff Abstract We point out that during the supernova II type explosion the thermodynamical conditions of stellar matter between the protoneutron star and the shock front correspond to the nuclear liquid–gas coexistence region, which can be investigated in nuclear multifragmentation reactions. We have demonstrated, that neutron-rich hot heavy nuclei can be produced in this region. The production of these nuclei may influence dynamics of the explosion and contribute to the synthesis of heavy elements. 2004 Elsevier B.V. All rights reserved. PACS: 25.70.Pq; 26.50.+x; 26.30.+k; 21.65.+f In recent years significant progress has been made nucleons and lightest clusters (vaporisation). These by nuclear community in understanding properties of different intermediate states can be understood as a highly excited nuclear systems. Such systems are rou- manifestation of the liquid–gas type phase transition tinely produced now in nuclear reactions induced by in finite nuclear systems [1]. A very good description hadrons and heavy ions of various energies. Under cer- of such systems is obtained within the framework of tain conditions, which are well studied experimentally, statistical multifragmentation model (SMM) [2]. the intermediate nuclear system is produced in a state According to present understanding, based on nu- close to statistical equilibrium. At low excitation en- merous theoretical and experimental studies of multi- ergies this is nothing but a well-known compound nu- fragmentation reactions, prior to the break-up a tran- cleus. At excitation energies exceeding 3 MeV per nu- sient state of nuclear matter is formed, where hot nu- cleon the intermediate system first expands and then clear fragments exist in equilibrium with free nucle- splits into an ensemble of hot nuclear fragments (mul- ons. This state is characterized by a certain tempera- tifragmentation). At excitation energies above 10 MeV ture T ∼ 3–6 MeV and a density which is typically per nucleon the equilibrated system is composed of 3–5 times smaller than the nuclear saturation density, −3 ρ0 ≈ 0.15 fm . Theoretical calculations [2] show that relatively heavy fragments may survive in the liquid– E-mail address: [email protected] (A.S. Botvina). gas coexistence region. In thermodynamic limit these 0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2004.01.064 234 A.S. Botvina, I.N. Mishustin / Physics Letters B 584 (2004) 233–240 heavy fragments would correspond to the infinite liq- itrons (e+) under condition of electric neutrality. In uid phase [3]. This statistical picture of multifragmen- supernova matter there exist several reaction types re- tation is confirmed by numerous experimental obser- sponsible for the chemical composition. At low densi- vations, such as an evolution of the fragment mass ties the most important ones are: distribution with energy (temperature), fragment cor- relations revealing the critical behavior, anomaly in the (1) neutron capture and photodisintegration of nuclei caloric curve, and by many others (see, e.g., [2,4–6]). + → + + Recent experiments (e.g., [7]) directly confirm that (A, Z) n (A 1,Z) γ, primary fragments are really hot, their internal excita- (A, Z) + γ → (A − 1,Z)+ n; (1) tion energy may reach up to 3 MeV per nucleon. Prop- (2) neutron and proton emission by hot nuclei erties of these hot nuclei can be extracted from multi- fragmentation reactions and used in analyzes of other (A, Z) → (A − 1,Z)+ n, physical processes, where similar nuclei are expected (A, Z) → (A − 1,Z− 1) + p; (2) to be produced. In this Letter we are going to use the knowledge (3) weak processes induced by electrons/positrons accumulated from multifragmentation studies for bet- and neutrinos/antineutrinos ter understanding nuclear physics associated with col- + − ↔ − + lapse of massive stars and supernova type II explo- (A, Z) e (A, Z 1) ν, + sions. More specifically, we consider the possibility of (A, Z) + e ↔ (A, Z + 1) +˜ν. (3) producing hot heavy nuclei in a protoneutron star, and in hot bubble between the protoneutron star and the The characteristic reaction times for neutron capture, shock front [8]. This region is crucial for success (or photodisintegration of nuclei and nucleon emission failure) of the supernova explosion. The presence of can be written as hot nuclei will influence many processes. For exam- −1 τcap = σnAvnA ρn , ple, the electron capture on nuclei plays an important −1 role in supernova dynamics [9]. In particular, the elec- τγA = σγAvγA ργ , tron capture rates are sensitive to the nuclear compo- τ = h/Γ¯ , sition and details of nuclear structure (see, e.g., [10]). n,p n,p The neutrino-induced reactions are very sensitive to respectively. Here σnA and σγA are the correspond- the nuclear structure effects and properties of weak in- ing cross sections, vnA and vγA are the relative (in- teractions in nuclei (see, e.g., [11]). It is also important variant) velocities, and Γn,p is the neutron (proton) that the presence of nuclei favors the explosion via the decay width. Our estimates show that at tempera- energy balance of matter in the bubble [12]. tures and densities of interest these reaction times In the supernova environment, as compared to the vary within the range from 10 to 106 fm/c,thatis nuclear reactions, several new important ingredients indeed very short compared to the characteristic hy- should be taken into consideration. First, the matter drodynamic time of a supernova explosion, about 100 at stellar scales must be electrically neutral and there- ms [8]. The nuclear statistical equilibrium is a reason- fore electrons should be included to balance positive able assumption under these conditions. However, one nuclear charge. Second, energetic photons present in should specify what kind of equilibrium is expected. −5 hot matter may change nuclear composition via pho- For densities ρ>10 ρ0 and for the expected tem- tonuclear reactions. And third, the matter is irradiated peratures of the environment, T 5 MeV, we obtain by a strong neutrino wind from the protoneutron star. τγA τcap, τn,p, i.e., the photodisintegration is less Below we apply a grandcanonical version [13] of the important than other processes. There exists a range of −5 SMM to calculate mass and charge distributions of nu- densities and temperatures, for example, ρ 10 ρ0 −3 clear species under these conditions. at T = 1MeV,andρ 10 ρ0 at T = 3MeV,where We consider macroscopic volumes of matter con- the neutron capture dominates, i.e., τcap <τn,p.Un- sisting of various nuclear species (A, Z), nucleons der these conditions new channels for production and (n = (1, 0) and p = (1, 1)), electrons (e−) and pos- decay of nuclei will appear (e.g., a fast break-up with A.S. Botvina, I.N. Mishustin / Physics Letters B 584 (2004) 233–240 235 = = emission of α-particles or heavier clusters) which re- Q i Qi and lepton number L i Li of the store the detailed balance. We expect that in this sit- system. This gives uation an ensemble of various nuclear species will = + be generated like in a liquid–gas coexistence region, µAZ AµB ZµQ, as observed in the multifragmentation reactions. Here µe− =−µe+ =−µQ + µL, the nuclear system is characterized by the tempera- µν =−µν˜ = µL. (5) ture T , baryon density ρB and electron fraction Ye (i.e., the ratio of electron and baryon densities). One These relations are also valid for nucleons, µn = µB may expect that new nuclear effects come into force and µp = µB + µQ.Ifν and ν¯ escape freely from the in this environment. For example, at high tempera- system, the lepton number conservation is irrelevant ture the masses and level structure in hot nuclei can and µL = 0. In this case two remaining chemical po- be different from those observed in cold nuclei (see, tentials are determined from the conditions of baryon e.g., [14]). number conservation and electro-neutrality: The weak interaction reactions are much slower. B ρ = = Aρ , The direct and inverse reactions in Eq. (3) involve B V AZ both free nucleons and all nuclei present in the matter. AZ It is most likely that at early stages of a supernova Q ρ = = Zρ − ρ = 0. explosion neutrinos/antineutrinos are trapped inside Q V AZ e AZ the neutrinosphere around a protoneutron star [15]. In = − − + this case we include the lepton number conservation Here ρe ρe ρe is the net electron density. The pressure of the relativistic electron–positron gas can condition by fixing the lepton fraction YL. Out of be written as the surface of the neutrinosphere one should take into account the continuous neutrino flux propagating 4 2 4 = µe + πT + 7 πT through the hot bubble. Due to large uncertainties in Pe 2 1 2 12π µe 15 µe the weak interaction rates, below we consider three m2 πT 2 physically distinctive situations: − e + 2 3 , µe µe (1) fixed lepton fraction YL corresponding to a where first order correction due to the finite electron β -equilibrium with trapped neutrinos inside the mass is included. The net number density ρe and neutrinosphere (early stage); entropy density se can be obtained now from standard Y β (2) fixed electron fraction e but without -equilib- thermodynamic relations as ρe = ∂Pe/∂µe and se = rium inside a hot bubble (early and intermediate ∂Pe/∂T .
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