Photonuclear reactions and astrophysics

B. S. Ishkhanov∗ Department of Physics, Lomonosov Moscow State University, Moscow, 119991 Russia and Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991 Russia

V. N. Orlin, K. A. Stopani, and V. V. Varlamov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991 Russia (Dated: Compiled on March 7, 2013) Photonuclear reactions play a prominent role in the nucleosynthesis processes in stars and in the Early Universe. Traditional and modern methods of studying photonuclear reactions are considered. Different factors which determine accuracy of photonuclear data are discussed. Cross sections of photonuclear reactions relevant to astrophysics are given.

Contents

Introduction 2

I. Main sources of photons in cosmic space and stars 3

II. Experimental study of photonuclear reactions 4

III. Analysis of discrepancies in photonuclear data 6

IV. Photonuclear reactions description in a combined model 8

V. Evaluation of photonuclear data 11

VI. Interaction of photons with atomic nuclei 12

VII. Primordial nucleosynthesis 15

VIII. e-process 16

IX. Photodisintegration of the iron peak nuclei 19

X. p-nuclei 22 Photodisintegration of Ta isotopes 23 Photodisintegration of Hg isotopes 26

XI. Photofission 29

Conclusions 31

Acknowledgments 31

References 31

∗Electronic address: [email protected] 2

Introduction

The world is composed of different chemical elements and their compounds. One of the fundamental questions of modern natural science is to determine the mechanism of production of chemical elements. This problem lies at the border between astrophysics and nuclear physics. Important information about the origin of chemical elements can be extracted from analysis of their abundances (Fig. 1).

FIG. 1: Schematic representation of the chemical element abundance curve in the Solar system.

Eight principal processes responsible for production of chemical elements were discussed in [1].

1. Hydrogen burning. This is the main process that provides long-term energy release in stars. During burning four hydrogen nuclei combine producing one 4He nucleus. This process occurs either in the pp-chain of nuclear reactions or in the CNO cycle of nuclear reactions involving heavier nuclei: C, N, O, Ne, etc., acting as catalysts. Also certain light nuclei are produced in reactions that involve protons. 2. Helium burning. Once helium is accumulated in the star, due to gravitational force the helium core shrinks and becomes sufficiently hot, initiating the process of helium burning. The 12C, 16O, 20Ne nuclei are formed during helium burning. 3. α-process. This is a process of successive captures of α-particles by a 20Ne nucleus, resulting in the formation of 24Mg, 28Si, 32S, 36Ar, 40Ca. The α-process is responsible for high abundances of the Nα-type nuclei, where α is the 4He nucleus, N is an integer. 4. e-process. This is a process of production of the iron peak nuclei at very high temperatures and densities under thermodynamic equilibrium conditions. 5. s-process. A process of slow successive neutron captures, that is responsible for production of nuclei heavier than iron. The rate of the s-process is commensurate with the rate of beta decays of unstable nuclei produced by the neutron capture reactions. The time scale of the s-process is 102—105 yr. The s-process is responsible for the nuclear abundance peaks at A ∼ 98, 138, and 208. 3

6. r-process. This is a process, in which nuclei heavier than iron are formed in a series of rapid successive neutron captures at a rate significantly faster than the rate of beta decays of resulting unstable nuclei. A typical length of the r-process is 0.01—100 sec. The maxima at A = 80, 130, and 195 in the nuclear abundance curve are a result of the r-process. 7. p-process. Production of a number of proton-rich isotopes with low abundances as compared to the nearby normal and neutron-rich isotopes. The likely mechanism of p-nuclei production involves the (p,γ) and (γ,n) reactions. 8. X-process. This is a nucleosynthesis process responsible for production of the 6,7Li, 9Be, 10,11B isotopes. It is believed that these elements are produced in disintegration reactions triggered by cosmic ray particles.

The set of nuclear reactions that take place in a star at thermodynamic equilibrium is governed by the stellar mass (table I). The temperature and density of a M = 25M star at different stages of nuclear processes are shown in Fig. 2.

TABLE I: Allowed nuclear reactions in stars

Mass, M Reactions 0.08 No 0.3 Hydrogen burning 0.7 Hydrogen and helium burning 5.0 Hydrogen, helium, and carbon burning 25.0 All fusion reactions with energy release

FIG. 2: Schematic diagram of chemical element production in a star.

The most important reactions of nucleosynthesis are induced by protons, neutrons, and α-particles. However, an important role is also played by the reactions triggered by non-thermalized photons, or photonuclear reactions. This review concentrates on the modern status of research in the field of photon-nucleus interactions relevant to the subject of stellar nuclear reactions.

I. MAIN SOURCES OF PHOTONS IN COSMIC SPACE AND STARS

There are several principal sources of sufficiently high-energy photons in stars and in cosmic space:

• annihilation of particles and antiparticles produced in the Big Bang; 4

• bremsstrahlung radiation from electrons and positrons; • inverse Compton scattering of photons on high-energy electrons; • the π0 → γ + γ decay; • gamma transitions between excited nuclear states; • scattering of the cosmic microwave background photons on high-energy nuclei; • acceleration of electrons in non-homogeneities of interstellar plasma; • gamma radiation from supernovae and active galaxy kernels.

The energies of the photons produced during these cosmic processes are distributed in a broad energy range from 10−1 to 107 keV. In thermodynamic equilibrium with stellar medium the energy of radiation is described by the Planck’s law. The number of photons with kinetic energy E in a unit volume of phase space

 1 3 E2 1 n = , (1) c π2  E  ~ e kT − 1 where T is the temperature of the stellar matter.

II. EXPERIMENTAL STUDY OF PHOTONUCLEAR REACTIONS

Systematic studies of photonuclear (primarily photoneutron) reactions started in the 50s. As the photon-nucleus interaction is purely electromagnetic and can be effectively calculated and explained, reactions of this kind provide definite advantages in what concerns their description and interpretation in comparison with charged particle reactions. But at the same time experimental studies of photon interaction with atomic nucleus pose many specific difficulties. The most important of them is the absence of intensive monoenergetic photons in nature, so experimentalists from the beginning tried to devise various techniques to get sources of nearly quasimonoenergetic photons. Historically the first were the experiments using bremsstrahlung beams produced by electron accelerators. The intensities of bremsstrahlung beams were sufficiently high and good statistical accuracy of results could be achieved. The energy spectrum of bremsstrahlung photons is continuous. That means that at a given end-point energy Emax one can measure directly only the reaction yield

Emax α Z N(Emax) = σ(E)W (Emax,E) dE, (2) D(Emax)ε 0 where σ(E) is the reaction cross section at the photon energy E, W (Emax,E) is the bremsstrahlung spectrum with end-point energy Emax, N(Emax) is the number of reaction events, D(Emax) is gamma-dose,  is detector efficiency, α is a normalization constant. To determine σ(E) several specially developed methods for unfolding were conventionally applied. The most widely used were the inverse matrix method and the regularization method. In such an approach one needs to solve a mathematically complicated inverse problem to obtain reaction cross section information from reaction yields, so in the 1960s an alternative method was introduced. It is based on the phenomenon of relativistic positron annihilation in flight. The spectrum of quasimonoenergetic annihilation photons is nearly Gaussian, with sufficiently small width (approximately several hundred keV). Due to the fact that positron annihilation photons are mixed with positron bremsstrahlung, a three-stage difference experiment strategy was needed. At the first stage the yield Y (Emax)e+ of the reaction induced by both annihilation and bremsstrahlung photons is measured. At the second stage the yield Y (Emax)e− of the reaction is measured using bremsstrahlung radiation from the electron beam. At the third stage the results are normalized, and under assumption that bremsstrahlung spectra for electrons and positrons are identical the cross section of the reaction triggered by quasimonoenergetic photons is obtained as a result of subtracting the latter measurement from the first one

σ(E) = Y (Emax)e+ − Y (Emax)e− . (3) As the intensity of quasimonoenergetic photon beams was very low statistical accuracy of the measurements was poor. 5

Only few measurements of total photoneutron reaction cross section measurements were performed using actual monoenergetic photons, that is, tagged photons obtained in very complex and low intensity experiments using coin- cidences of outgoing photons and scattered electrons. Recently more advanced methods have become to be actively used in different laboratories to study photonuclear reactions at the energies close to the nucleon separation energy. Experiments using continuous-energy bremsstrahlung combined with the induced activity measurement technique are perfectly suited to carry out systematic surveys on various types of photonuclear reactions. The complete sys- tematics of groundstate reaction rates of numerous isotopes were studied at the High Intensity Photon Setup (HIPS) of the superconducting linear electron accelerator S-DALINAC facility at the Technishe Universitat Darmstadt [2, 3]. Continuous-energy bremsstrahlung was produced by fully stopping a monoenergetic electron beam in a thick copper radiator target. Due to the high currents of up to 40 µA, the photon intensity reaches maximum values of about 7 −1 −1 −2 10 keV s cm at 80% of the maximum emergy Emax. A lot of data on resonance fluorescence (photon scattering) near photonucleon reaction thresholds was obtained in this way. Many results for heavy elements behind the so-called iron peak, mainly produced in neutron capture processes, were obtained. A bremsstrahlung facility of superconducting electron accelerator ELBE (Electron Linear accelerator of high Bril- liance and low Emmittance) of FZ Dresden-Rosendorf [4] was extensively used for photon scattering and activation studies and experimental measurements of photodisintegration rates of heavy nuclei. Energies of up to 20 MeV with average currents up to 1 mA were available, which was appropriate for probing photon-induced reactions. Studies of (γ,n), (γ,p), and (γ,α) on many nuclei were carried out via photoactivation technique. Recently a new experimental method using a laser-Compton backscattering (LCS) gamma-ray beam in combination with an active target technique became a promising tool for precise measurements of low-energy photon-induced nu- clear reactions relevant to nucleosynthesis. The latest development of LCS gamma-ray beams follows the development of gamma-ray sources, bremsstrahlung, and positron annihilation in flight. Direct determination of photodisintegra- tion cross sections using such gamma-ray sources may shed new light on nucleosynthesis. New experimental results with absolute cross sections of photodisintegration of nuclei in the gamma-ray energy range up to 30 MeV, where serious discrepancies existed in previously taken data, were obtained at the gamma-ray source of the New SUBARU synchrotron radiation facility of the University of Hyogo in Japan [5, 6]. Determination of the cross sections of photonuclear reactions with several neutrons in the final state poses a serious problem. If the reaction produces beta-unstable nuclei, the problem of separating channels with different multiplicities can be overcome by using the gamma-activation technique. A setup of this kind was created at the Skobetlsyn Institute of Nuclear Physics at the Lomonosov Moscow State University (Fig. 3).

FIG. 3: Scheme of the experiment in a beam of bremsstrahlung gamma rays.

An electron beam produced by the RTM-70 racetrack microtron [7] interacts with a tungsten target and produces bremsstrahlung radiation. The studied sample is placed directly behind the bremsstrahlung target. Bremsstrahlung photons induce excitations of the nuclei of the studied target with energies E∗ ≤ 70 MeV. Nucleon emission, which occurs during GDR decay, results in production of isotopes, that were not initially present in the sample, some of which are unstable. 6

When these nuclei eventually decay, the daughter nuclei can be produced either in a ground state or in an excited state with corresponding probabilities. De-excitation of the excited states leads to emission of photons. The gamma ray spectra of induced activity produced in nuclear beta decays are unique for each isotope. After the irradiation the induced activity spectrum is measured using a high-purity germanium detector. The peaks corresponding to detection of induced activity photons are resolved in the spectrum and identified by their energy and the rate of change of the amplitudes. Activation technique allows to calculate yields of nuclear reactions, that is, convolution of the reaction cross section and the spectrum of incident particles defined in (2). The reaction yield is essentially a rate of nuclear reactions in the target, and it determines the rate at which the final nuclei are produced in the reaction. If these reaction products are unstable, they at the same time decay at a certain rate according to the radioactive decay law. Besides, some other unstable nuclei may decay into them, thus providing another source of their production. The activity A of a particular unstable nucleus produced in a nuclear reaction under study, therefore, depends on time and reaction yield: A = A(t, Y ). If the activities are measured at certain points in time, the unknown yields can be obtained. This technique was used to measure yields of photonuclear reactions with multiple (1—7) outgoing neutrons.

III. ANALYSIS OF DISCREPANCIES IN PHOTONUCLEAR DATA

It follows from the above description that there is a lot of total and partial reaction cross section data obtained in fundamentally different experiments. The consequence is that there are significant disagreements both in shape and value among reaction cross sections obtained in different laboratories using different methods. For example, as a rule cross sections obtained using bremsstrahlung have much more pronounced structure in comparison with those obtained using quasimonoenergetic annihilation photons (Fig 4).

FIG. 4: A comparison of (γ,xn) reaction cross sections obtained using bremsstrahlung (line) and annihilation photons (dots).

The problem of electric giant dipole resonance (GDR) structure, i.e. the presence of distinct powerful maxima in cross sections of photonuclear reactions—first of all total photoabsorption reactions—is closely connected with effective energy resolution achieved in various experiments. The second serious question of photonuclear research is that of measuring partial reaction cross sections in ex- periments employing neutron detectors. Various partial reactions with different numbers of outgoing neutrons can occur depending on the photon energy—(γ,n), (γ,2n), (γ,3n), and so on. That means that if the outgoing neutron is detected in an experiment without using extremely complex coincidence-based procedures, then only the total neutron yield reaction cross section σ(γ, xn) = σ(γ, n) + 2σ(γ, 2n) + 3σ(γ, 3n) + ... (4) can be obtained. This is different from the total photoabsorption reaction cross section which equals to a sum of total neutron and proton reactions σ(γ, abs) = σ(γ, n) + σ(γ, np) + σ(γ, 2n) + σ(γ, 3n) + ... + σ(γ, p) + σ(γ, 2p) + ... (5) and is of the most interest. Accurate neutron multiplicity sorting is essential to determine its value. Absolute majority of partial photoneutron reaction cross sections was obtained using neutron multiplicity sorting methods in 7 experiments at the National Lawrence Livermore Laboratory (USA) and at the France Centre d’Etudes´ Nucl´eaires de Saclay using quasimonoenergetic annihilation photon beams. It is important to underline that the methods used in both laboratories for photoneutron multiplicity sorting were quite different. Absolute values of total neutron yield reaction cross sections (γ,xn) obtained in Livermore using quasimonoenergetic photons are in general smaller by about 12% in comparison with corresponding data obtained using analogous photon beams in Saclay and using bremsstrahlung in other laboratories. The main reasons of such disagreements are rather large uncertainties in photon flux and detector efficiency measurements. Much more pronounced are disagreements among partial reaction cross sections σ(γ, n), σ(γ, 2n), σ(γ, 3n),... (Fig. 5). Generally and briefly—all (γ,n) cross sections are larger in Saclay (squares), but all (γ,2n) cross sections (triangles)—at Livermore with the magnitude of disagreements being as high as 60%.

FIG. 5: Systematics of Saclay/Livermore disagreements for (γ,n) [squares] and (γ,2n) [triangles] reaction cross sections. Inte- grated cross section ratios are shown.

The most widely used experimental method of neutron multiplicity sorting and separation of reactions with different numbers of outgoing neutrons, which was used both in Livermore and Saclay, is based on the main assumption that the kinetic energy of the (γ,2n) reaction neutrons is less than the kinetic energy of a single neutron produced in the (γ,n) reaction. However, quite different methods were used to measure neutron kinetic energy: the so called “ring-ratio” method (concentric rings of BF3-counters embedded into paraffin or polyethylene) in Livermore and a calibrated large Gd-loaded liquid scintillator in Saclay [8]. The differences of arrangement mean that the methods of obtaining the cross sections were different, resulting in complex systematic discrepancies mentioned above. A lot of data for total and partial photonuclear (primarily, photoneutron) reaction cross sections were obtained in the 1970s and 1980s and the results were included in various reviews [8], atlases [9, 10] and databases [11, 12]. Because of that studies of corresponding systematics, development of methods of overcoming the disagreements, and evaluation of reliable data for both total and partial reaction cross sections present a significant interest and are among important fields of data processing activity of the Centre for Photonuclear Experiments Data (Centr Dannykh Fotoyadernykh Eksperimentov—CDFE) participating in the Nuclear Data Centers Network under auspice of the International Atomic Energy Agency. Because data of both laboratories agree as to total number of neutrons detected, it was proposed [13–15] that the differences in their reaction cross sections σ(γ, n) and σ(γ, 2n) arose from the process of sorting the counts as 1n and 2n events (neutron multiplicity sorting). Special objective criteria of data reliability were introduced [16, 17]. Systematic research revealed many physically non-reliable data points in certain energy regions. A new so-called “experimentally-theoretical” approach for data evaluation, free from neutron multiplicity sorting shortcomings, was proposed [18–21]. The method is based on using equations of combined model of photonuclear reactions for separation of initial total neutron yield reaction cross section into partial reaction cross sections free from neutron multiplicity sorting problems. где  — постоянная распада образующегося в результате реакции изотопа, n — процентное содержание исходных ядер в образце,  — эффективность регистрации германиевым детектором соответствующей гамма-линии в спектре остаточной активности образовавшихся изотопов,

ti — время облучения, td — время между концом облучения и началом

измерения спектра, tm — продолжительность измерения спектра, А — количество отсчетов детектора, соответствующих выбранной гамма-линии спектра остаточной активности образца, I — интенсивность линий в спектре гамма-квантов дочерних ядер, образующихся при бета-распадах продуктов реакций. При расчетах использовались интенсивности гамма- 8 переходов [57], полученные при помощи интерфейса [56]. С помощью  -активационной методики были измерены выходы IV. PHOTONUCLEAR REACTIONS DESCRIPTION IN A COMBINED MODEL различных реакций с образованием до 7 нейтронов в конечном состоянии. To describe cross sectionsНиже of мы multiparticle приведем некоторые photonucleon из полученных reactions результатов and energy для spectra изотопов of emitted photonucleon, a combined model (CM) ofHg, photonucleon Ta, Pd и 238U. reactions is used, which includes the following set of models (Fig. 6): 1) semimicroscopic model of nuclear vibrations (SMV), 2) quasideuteron model (QM), 3) exciton model (EXM) and 4) evaporation model (EVM). 6. A combined model of photonuclear reactions Semimicroscopic model Photonuclear of nuclear vibrations reaction cross Combined model of sections Quasideuteron model photonuclear reactions Exciton model Photoneutron and photoproton spectra Evaporation model

Combined model of photonuclear reactions (CMPR) includes the FIG. 6: Combined model offollowing photonuclear set of reactionsmodels: 1) (CM) semimicroscopic includes the model following of nuclear set of models: vibrations 1) semimicroscopic model of nuclear vibrations (SMV), 2)(SMV quasideuteron), 2) quasideuteron model (QM), model 3)(QM exciton), 3) modelexciton (EXM) model and(EXM 4)) evaporationand 4) model (EVM). evaporation model (EVM). Four components of the CM describe all stages of a photonucleon reaction starting from absorption of a photon 6.1. Semimicroscopic model of nuclear vibrations and ending with a nucleon emission.In the region However, of low energies simple mechanical( E  40 MeV) union the elec oftric these giant modelsresonances is not possible. Before that it is necessary to solve three problems: estimate the widths of giant resonances (GR) described by the SMV, without (GR) — a coherent mixture of single-particle-single-hole (1p1h) excitations — which it is impossible to obtainare formed a cross. The sectionmost powerful of the of photoabsorption; these is the isovector then giant it dipole is necessary resonance to take into account in the framework of the exciton and evaporation models the isospin effects, which play an important role in description of the proton channel of the giant dipole resonance decay; and finally, collective aspects of input 1p1h-dipole states with the statistical nature of the exciton model need to be agreed upon, so it is possible to use the CM for description of photodisintegration of exotic nuclei far from the valley of beta-stability. In the region of low energies (Eγ < 40 MeV) the electric giant dipole resonance, or GDR—a coherent mixture of single-particle-single-hole (1p1h) excitations—is formed. The GDR largely determines the properties of photonuclear reactions at low energies. Apart from the GDR, as the study of the angular distributions of photonucleons shows, in the region E ∼ 25–35 MeV it is also necessary to consider the effect of the isovector giant quadrupole resonance (IVGQR) and the first overtone GDR (GDR2). In long wave approximation the integrated cross section of a sufficiently narrow resonance |αi for the electric L isovector absorption with the multipolarity J = L, S = 0, T = 1, Tz = 0, π = (−1) can be written as

2π3e2 L + 1 X σ (EL, α) = E2L−1 |hα, M|F (E )|0i|2, (6) int ( c)2L−1 L[(2L + 1)!!]2 res LM10 res ~ M where the isovector induced field A " ! # X k2 r2 F (E ) = 2t 1 − res + ··· rLY (ˆr) , (7) LM1µ res µ 2(2L+3) LM i=1 i

Eres is the resonance energy, kres = Eres/(~c) is the momentum transferred to the nucleus. The main modes of isovector EL-vibrations are associated with the probe operator FLM1µ = FLM1µ(0), that is the first member of the decomposition of the FLM1µ(Eres) operator. A simple vibration Hamiltonian with separable multipole-multipole forces [22] is used in the SMV to describe the energy-degenerate M-oscillations in a spherical nucleus: X 1 X H = ε c+ c + F + F , (8) L L,µ L,µ L,µ 2κL L01µ L01µ µ µ

+ where cL,µ is quasiboson operator of creation of the initial excitation characterized by the angular moment of J = L, M = 0 and the isospin τ = 1 µ = 0, ± 1 corresponding to the group of degenerate single-particle transitions from filled (β) to free levels (α) oscillator potential with the energy transition  N − Z  ε = L ω + µ V − E (9) L,µ ~ 1 A Coul 9

−1/3 (~ω = 41A MeV is the excitation energy of quanta of oscillator potential, V1 ∼ 100 MeV is the symmetry potential of the nucleus and ECoul is the average Coulomb energy of one proton). Diagonalization of the Hamiltonian (8) allows one to find the energy and the probability of excitation of the photoresonance, its total cross-section and the isospin splitting. The interaction constant κL is connected with symmetry potential V1 by formula

2L κL = πV1/(A < r >). (10) To obtain realistic values of the resonance energies of isovector EL-resonances and their overtones, the value of V1 was normalized to the experimental data for the GDR energy, which were approximated by the hydrodynamic relation, taking into account the diffuseness of the nuclear surface:

q 2 2 2 2 4 4 −1/3 Edip ≈ 86 (1 + π ξ )/(1 + 10π ξ /3 + 7π ξ /3) A MeV, (11)

−1/3 where ξ = a/R0, a ≈ 0.55 fm and R0 ≈ 1.07A fm. The secondary resonance GDR2 is caused by 3~ω-single-particle transitions induced by the term proportional to 3 r Y1M (ˆr) in the vibrational field F1M10(ECoul) (see (7)). This term, however, leads also to low-energy 1~ω-excitations. To separate the high-energy vibrations from low-energy, the following was used as a probe field

A X 2 F1M10(η) = (τz(η − r ) rY1M (ˆr))i, (12) i=1 where the constant η is chosen so that the sum of oscillator forces for the lower resonance is minimal. In a spherical nucleus oscillations with M = 0, which exhausts one-third of the sum of oscillator strength for F1M10-vibrations, can be approximately described by the Hamiltonian 1 H = ωc+c + 3 ωc+c + (η)F (η)F+ (η), (13) ~ 1 1 ~ 2 2 2κ 1010 1010 where interaction constant is given by πV (η) = 1 . (14) κ A [η2hr2i − 2ηhr4i + hr6i]

Diagonalizing Hamiltonian (13) one can determine energies and probability amplitudes for the normal modes of + vibrationc ˆk |0i, k = 1, 2. GDR2 corresponds to such a choice of the parameter η at which almost all power F1M10(η)- + 208 transitions are concentrated in the upper resonance |overti =c ˆ2 |0i. For the nucleus Pb, this is achieved with a 2 value of η = 51.6 fm . In this case the energy of Eovert = 32.5 MeV. Substituting state |overti in the formula (6), we find the integrated GDR2 cross section. The width of GDR is estimated using a semi-empirical curve approximating the experimental data:

 2 2 2 2  2 2 2 ΓGDR ≈ 0.0293 1 − 3ξ(1 + π ξ /3)/(1 + π ξ ) /(1 + π ξ )ECoul, MeV, (15)

−1/3 where ξ ≡ a/R0, a ≈ 0.55 fm and R0 ≈ 1.07A fm. The widths of the remaining GR were determined by the exciton model. > In the region Eγ ∼ 40 MeV above the giant resonance, the quasideuteron (QD) photoabsorption mechanism becomes dominant. According to this mechanism, the excited nucleon exchanges a virtual pion with a neighboring nucleon, with the result that it is a correlated proton-neutron pair rather than a single nucleon that receives the energy and momentum from the absorbed photon. In the present study, the approximation from [23] was used. The process of photonucleon emission from medium and heavy nuclei can be roughly divided into two stages: pre-equilibrium and evaporation. They are characterized by two main functions: P (U; m, A)—by a probability density of the formation of an m- exciton state with energy U in some intermediate nucleus A and P(U, A)—by a probability density to achieve thermal equilibrium in this nucleus. Preequilibrium nucleon emission becomes insignificant long before the equilibration moment; therefore, we will neglect inverse transitions (m → m − 2) in the following. The probability densities P (U; m, A) and P(U; A) can be computed using recurrence relations, connecting them with the probabilities of formation of exciton and equilibrium states in the earlier stages of the reaction, given that 10 target nucleus P (U; m0,A0) = δ(U − E) and P(U; A0) = P (U;m, ¯ A0)δ(U − E)(m0 is the initial number of excitons andm ¯ is the average number of excitons in thermal balance). We use common formulas for the probability density of the nucleon emissions per unit of time of the m-exciton and equilibrium states:

2s+1 inv ω(U; m−1) λemiss(ε, E; m) = µεσk (ε) , λevap(ε,E) = N(E)εσinv(ε)w(U) (16) π2~3 ω(E; m) and for the rate of intranuclear transitions m → m + 2:

↓ 2 ~Γ (E; m) = 2πM ω+(E; m) (17)

Density of the m-exciton states ω(E; m), ω+(E; m) calculated in the framework of the Fermi gas model and the total density of nuclear levels of w(U) are calculated from the Hilbert-Cameron compositional formula [24]. Using the functions P (U; m, A) and P(U; A) one can determine such characteristics of photodisintegration nucleus as cross-sections of photonucleon reactions with emission of an arbitrary number of nucleons, the photonucleon energy spectra integrated over angle, and also separate the contributions of the pre-equilibrium and evaporation processes to the reaction. Considering the GDR channel of photonucleon reactions, it is necessary to take into account isospin effects (see Fig. 7). This is because the T>-components of the giant dipole resonance decay predominantly via proton emission.

FIG. 7: The CM-calculated cross sections of (γ, n)- and (γ, p)-reactions for the 48Ca nucleus with (solid curves) and without (dashed curves) the isospin effects corrections. Experiment [25].

Within the model being considered, one can take into account isospin effects by modifying, for the neutron T>- channel of the reaction, the densities of exciton states ω(U; m) and the total densities of states w(U) formed after the emission of the nucleon using the substitution U → U−∆T , where ∆T is the excitation energy of the first level of the final nucleus, whose isospin is greater by unity than the isospin of the nucleus in the ground state. The above substitutions permit taking into account the fact that the densities of T>-states are lower than the total densities of states because of their upward shift along the energy scale by about ∼ ∆T . We note that it is necessary to change only the densities of final states, since, for the neutron T>-channel of the reaction, the densities of initial inv states and the cross section σn decrease in the same proportion in respect to their total values. Collective dipole states interact strongly with vibrations of the nuclear surface and as a result they decay mainly to collective 2p2h-like states “dipole phonon + surface quadrupole phonon”. This leads to the fact that in the initial intranuclear transitions the maximum energy of the scattered particle or hole is decreased by the value of the collective dipole shift ∆coll, causing a reduction in the spreading width of 11 the dipole state (see (17)). Taking into account that the degree of collectivization of the input 1p1h-states gradually decreases while the distance from the maximum resonance increases, approximately as R(E) = σGDR(E)/σGDR(Edip) we obtain the following estimate for the spreading width of the input 1p1h-state

↓ 2 Γ (E; 2) = 2πM ω+(E−R(E)∆coll; 2). (18) Collectivization of input 1p1h-states reduces yields of multiparticle photonucleon reactions in the GDR energy region for nuclei distant from the valley of beta stability (see Fig. 8).

FIG. 8: Influence of collective effects on the results of the calculation with the CM of the reaction cross section (γ, 2n)+(γ, 2n+p) for tin isotopes. The dark curve represents calculations taking into account collective effects, light curve — calculations ignoring these effects.

V. EVALUATION OF PHOTONUCLEAR DATA

As it was noted above, there is a serious problem of disagreements among partial photoneutron reaction cross section data provided by different experiments. The absolute majority of the data were obtained in Livermore (USA) and Saclay (France). In general the (γ,n) reaction cross sections are larger in Saclay, but those for the (γ,2n) reaction are larger in Livermore data and the difference can be as high as 60%. Since data from both laboratories agree in what concerns the total number of neutrons detected, it is clear that the disagreements arise from the neutron multiplicity sorting. Detailed studies of the data disagreements were undertaken in order to find objective criteria of data reliability and authenticity. Very simple, clear, direct, and absolutely objective criteria of simultaneous data reliability and authenticity of cross sections of the (γ,n), (γ,2n), and (γ,3n) reactions were proposed [16, 17]. The most interesting, important and effective of them is the transition multiplicity function F2:

F2 = σ(γ, 2n)/σ(γ, xn) = σ(γ, 2n)/σ[(γ, n) + 2(γ, 2n) + 3(γ, 3n) + ...]. (19)

The point is that from the definition it is absolutely clear that values “F2 > 0.50” signify physically unreliable values of σ(γ,2n) and, therefore, σ(γ,n) is also unreliable and hence multiplicity sorting was incorrect. Indeed, analogous functions F1,3,4,... that should not have values larger then 1.00, 0.33, 0,25,. . . respectively could be applied for additional data reliability analysis. Systematic research [16–21] revealed that many experimental cross sections obtained both at Saclay and Livermore did not satisfy the introduced criteria and, therefore, were not reliable. To evaluate reliable partial photoneutron reaction cross sections new experimentally-theoretical method based on equations of the combined photonuclear reaction model described above was proposed [16, 17]. The new approach uses only total neutron yield reaction cross sections σ(γ,xn), which are free from the neutron multiplicity sorting problems, as its input data. To separate the total neutron yield cross section into partial reaction cross sections transition multiplicity functions

theor Fi = σ(γ, in)/σ(γ, xn) = σ(γ, in)/σ[(γ, n) + 2(γ, 2n) + 3(γ, 3n) + ...]. (20) are used. Using these, reliable reaction cross sections are evaluated from the following formula:

eval theor exp σ (γ, in) = Fi (γ, in) × σ (γ, xn). (21) 12

Such processing insures that physically reliable competition of partial reactions is obtained in accordance with equations of the model and the sum of evaluated partial reaction cross sections is equal to the experimental data for total neutron yield cross section free from neutron multiplicity sorting problems. Data evaluated using such approach are in good agreement with experimental data obtained using alternative methods of neutron multiplicity sorting. One modern method of this kind is based on using a combination of a quasimonochromatic laser-Compton scattering gamma source and the ring-ratio neutron detection technique [26]. For example, in Fig. 9 our evaluated data for the 118Sn(γ,n)117Sn reaction [16] are compared with experimental data [26]. In Fig. 10 evaluated data for the 208Pb(γ,n)207Pb reaction cross section are compared with data from [27] and both Saclay and Livermore data, renormalized according to the IAEA recommendation. One can see that the data cleared from neutron multiplicity sorting agree with the LCS-data, which do not suffer from the multiplicity sorting problem, and that both of them disagree with Livermore (slightly) and Saclay (much more).

FIG. 9: Comparison between our evaluated FIG. 10: Comparison between our evalu- ([16] dots) and experimental (Saclay—squares, ated ([28] dots) and experimental (Saclay— Livermore—triangles, Utsunomiya [26]—stars) squares, Livermore—triangles, Utsunomiya [27]— data for the 118Sn(γ,n)117Sn reaction cross section stars) data for the 208Pb(γ,n)207Pb reaction cross near threshold. section near threshold.

Uncertainties of nuclear reaction cross sections obtained in laboratory measurements can lead to significant dis- agreements in calculations of the Solar System conditions. For example, extrapolation of experimental data from GDR energy region to the (γ,n) threshold region can increase uncertainties by an order of magnitude especially if there are resonance states near threshold. Thus, studies of the M1 and pigmy resonances are very important in this low-energy region. Additionally, a competition between nuclear decay channels with outgoing protons, neutrons, and photons should be taken into consideration for energies near the reaction threshold. New reliable partial reaction cross sections were evaluated for 115In, 112,114,116,117,118,119,120,122,124Sn, 159Tb, 181Ta, 188Os, 197Au, and 208Pb. Further we will discuss mainly the situation for energy range from the photonuclear reaction threshold up to about 50 MeV, where the GDR excitation mechanism dominates.

VI. INTERACTION OF PHOTONS WITH ATOMIC NUCLEI

The properties of the interaction between photons and atomic nuclei are known from laboratory experiments. There are two strong maxima in the energy dependence of photonuclear interaction cross section (Fig. 11). The first is in the energy range close to ≈ 20 MeV, and the second is at the ≈ 300 MeV energies. The first maximum corresponds to the GDR formation. In nuclear models of collective excitations the E1 resonance is a result of coherent oscillations of protons against neutrons caused by electromagnetic field of the photon. Figure 12 shows cross sections of total photoneutron yield reactions (γ,xn) in the GDR energy range for different nuclei. The position of the GDR maximum depends on the mass number A and monotonically decreases as the mass number increases:

E ≈ 78A−1/3MeV. (22) 13

FIG. 11: Schematic representation of the cross section of photonuclear interaction.

The integrated photoabsorption cross section in the GDR energy range gradually increases as the mass number A increases and is well approximated with the following expression: Z NZ σ = σ(E)dE ≈ 60 MeV · mb. (23) int A GDR

FIG. 12: (γ,xn) reaction cross sections in the energy range of the GDR. 14

The width of the GDR varies from 5 to 20 MeV depending on the properties of the nucleus. For axially symmetric nuclei there are two characteristic dimensions b and a—the semi-axes of the nuclear ellipsoid in longitudinal and transverse directions relative to the nuclear axis of symmetry respectively. For such nuclei, as it can be seen from the photoneutron cross section on 165Ho, the GDR maximum splits into two components: r r E = 78 0 MeV,E = 78 0 MeV, (24) a a b b where r0 = 1.3 fm. The width of splitting ∆E depends on the deformation of an axially-symmetric nucleus and is described by the following relationship:

−1/3 ∆E = Eb − Ea = 78A βMeV, (25) where β = (b − a)/R¯ is the nuclear deformation parameter, R¯ = 1.3A−1/3 fm. In the energy range of the GDR an excited nucleus decays mainly by emitting a proton, or one to three neutrons. At the energies greater than 300 MeV the photon wavelength is sufficiently short to interact with individual nucleons in a nucleus. The mean free path of such a photon is of the same order of magnitude as the nucleus size. Hence, photons move freely inside a nucleus and interact with all nucleons, so the total cross section of photon absorption is proportional to the mass number A. The maximum in the energy region around 300 MeV is called the ∆(1232) resonance. Its width is approximately 150 MeV. Its excitation corresponds to turning the spin of one of the quarks in a nucleon upside down. The ∆(1232) resonance decays into a nucleon and a π-meson:

∆ → N + π.

In the ∆(1232) resonance energy region photon scattering experiments were performed for a large number of nuclei. Values of the ratio of total photoabsorption cross-section to mass number A do not depend on A in the region of medium and heavy nuclei, which suggests that the assumption σtot = Aσ(γ, N) is valid [29]. Above the ∆(1232) resonance energies excited states of nucleons decay with emission of several outgoing mesons. In the excitation energy range between the energies of GDR and ∆(1232) resonances excited nuclei typically decay by emitting several nucleons. As the Coulomb barrier prevents emission of protons, typically 4—7 neutrons leave the nucleus. In the energy range close to the low-energy limit of the GDR (E < 6—8 MeV) there exists another type of collective nuclear excitations—the pygmy resonance, which is commonly interpreted as an oscillation of the neutron excess against the nuclear core in neutron-rich nuclei (N > Z). At low energies Eγ < 5—10 MeV there are distinct resonances corresponding to excitations of nuclear levels. The conditions under which nuclei interact with photons in stars are substantially different from those of a laboratory experiment. When the temperature of the medium is T > 108 K, the most nuclei are excited due to interactions with electrons and photons of the stellar plasma having energies of several keV. Relative populations of nuclear excited states are well approximated by the Maxwell-Boltzmann distribution law. The process of thermal population of nuclear excited states becomes significant as soon as the temperature becomes commensurate with excitation energies. This effect in particularly prominent in the case of odd nuclei with a large number of low-lying excited states. As a result, photonuclear reactions take place not only between photons and ground state nuclei but also between photons and excited nuclei with spins and parities different from those of the ground state. Numerous experiments were performed to extract the GDR width and its shape as functions of the nuclear tem- perature T . The phonon damping model√ [30] well described the GDR width including the increase of the width at T ≤ 3 MeV roughly proportional to T as well as a saturation plateau at high T . The position of the GDR (peak energy) remains roughly unchanged as T varies. A recent compilation of data about GDR built on excited states is given in [31]. Inside a star beta decay half-lives may vary. New beta decay channels open due to interactions of nuclei with electrons and positrons of the stellar plasma. Beta decay occurs not only from ground states but also from excited states of nuclei, which leads to considerable changes of half lives of isotopes. For example, the half life of the decay 99 5 of Tc from the ground state, measured under laboratory conditions, is T1/2 = 2.1 · 10 yr. At the temperature T > 3 · 108 K due to decays from excited states of 99Tc to excited states of 99Rh the half life is less than 10 yr. New beta decay modes also develop in stellar plasma. The “Continuum e−-capture” process is quite common, and often prevails over “orbital e−-captures” in highly-ionized stellar medium. Positron captures also gain importance for under stellar conditions, especially at high temperatures (T > 109 K). High concentration of positrons can be produced from the e− + e+ ↔ γ + γ equilibrium. Properties of the nuclei themselves also change. This is particularly important at the r-process stage of nuclei production. During supernovae explosions or in neutron stars densities of the stellar matter become as high as nuclear 15 densities, and such nuclear properties as binding energies, neutron and proton separation energies change. It is essential to know properties of nuclear matter under such extreme conditions for nuclei distant from the beta stability region, as they determine the mechanism of their production in r- and s-processes. Calculations in frameworks of different models were performed to describe the properties of nuclei under extreme conditions. There are several processes, where the role of photonuclear reactions in production of atomic nuclei has to be taken into consideration:

1. primordial nucleosynthesis; 2. e-process; 3. nuclear photodissociation in the iron peak region; 4. p-process; 5. fission.

VII. PRIMORDIAL NUCLEOSYNTHESIS

The discovery in 1965 of the 2.7 K microwave background provided a major support of the Big Bang model. By the first second after the Big Bang the Universe had evolved into an environment of interacting particles, turning into each other. In particular at photon energies greater than 200 MeV mutual transmutations of protons and neutrons takes place:

γ + p → ∆+ → n + π+ γ + n → ∆0 → p + π−. (26)

The medium consisted of photons, neutrinos, electrons, positrons, protons and neutrons. Photons were generated in annihilations of Big Bang particles and anti-particles. The ratio between numbers of photons and nucleons in the Early Universe was n γ ≈ 109. (27) nN The start of the primary nucleosynthesis was determined by the energy of background photons. Atomic nuclei were created in the Early Universe from protons and neutrons. The fraction of protons and neutrons in the total mass of the Universe is 2—5%. At the temperature T ∼ 109 K (and kinetic energies of ∼ 1 MeV) neutrons and protons transformed to each other due to the weak interactions

− p + e ↔ n + νe, (28)

+ p +ν ¯e ↔ n + e , (29)

− n ↔ p + e +ν ¯e (30) and were in a state of thermodynamic equilibrium. In thermodynamic equilibrium the probability of production of a neutron or proton with energy E is described by the Gibbs distribution. The initial reaction of the primordial nucleosynthesis is the deuterium production reaction (31). Accumulation of deuterium due to this reactions at this stage is prevented by its rapid breakup by photons in a photodissociation process. Deuterium binding energy is 2.22 MeV, and though the mean energy of photons has already fallen below this value, there were enough photons in the high-energy part of the spectrum that were able to break up the produced deuterium, as nγ ≈ 109. Therefore, the initiation of deuterium synthesis and of the whole nucleosynthesis chain nN was delayed up until the approximately 100th second after the Big Bang, when the mean kinetic energy of particles decreases to 0.1 MeV. The chain of the main 4He synthesis reactions (for each reaction Q is its energy):

2 p + n → 1H + γ, Q = 2.22 MeV, (31)

(3 2 2 1H + p, Q = 4.03 MeV, 1H + 1H → 3 (32) 2He + n, Q = 3.27 MeV, 16

2 3 4 1H + 1H → 2He + n, Q = 17.59 MeV, (33)

2 3 4 1H + 2He → 2He + p, Q = 18.35 MeV. (34) At the primordial nucleosynthesis stage the energy of background photons was high enough (Fig. 13) to break up produced nuclei, which was greatly facilitated by the ratio of photons to nucleons being of the order nγ = 109. nN

FIG. 13: Yields of light nuclei and barion density (solid curve) during the primordial nucleosynthesis stage.

Cross sections of the most important photonuclear reactions on 3H, 3He, 4He in the energy range below 60 MeV are shown in Fig. 14. Primordial nucleosynthesis and initial 4He abundance provide a source of information about the physics of the Early Universe. The photonuclear reactions d + γ → p + n and p + n → d + γ are the basic elements of subsequent chains of nuclei production. Further processes of production of nuclei with A > 5 take place in stars.

VIII. e-PROCESS

If the mass of a star M > 10M , then successively more and more heavy nuclei are produced in it due to nuclear fusion. The main processes here are successive α-particle captures

12C −→α 16O −→α 20Ne −→α 24Mg −→α 28Si (35) and fusion of carbon and oxygen 12C + 12C, 12C + 16O, and 16O + 16O. Each stage of production of increasingly heavy nuclei begins with gravitational collapse of a star, leading to its heating, which makes the fusion reactions allowed for nuclei with A > 16. At this stage of evolution of heavy stars an important role is played by numerous reactions with protons, neutrons, α-particles, and photons, which are available in sufficient quantities in the star due to reactions of photodisintegration of already produced nuclei. These reactions lead to production of elements in the region of the iron peak. As the temperature raises, along with an increase of the photon energy (Eγ ∼ T ) the number of photons also 4 increases (Nγ ∼ T ). Much earlier than the conditions of silicon nuclei fusion are met the energies and intensities of the photons are sufficient for the reactions of silicon photodisintegration:  24Mg + α (Q = −9.98 MeV),  28Si + γ → 27Al + p (Q = −11.58 MeV), (36) 27Si + n (Q = −17.18 MeV).

28Si and the produced high-Z nuclei irradiated in n, p, α, and γ fluxes form the majority of the nuclei of the iron peak. 17

FIG. 14: Cross-sections of photonuclear reactions on 2H, 3H, 3He, 4He, in the energy range below 60 MeV [11]. 18

At the temperature of ≈ 109 K nuclear reactions in stars can be divided into two groups. The first is the group of capture reactions with the rates of high-A nuclei production prevailing over the rates of their decay due to photons. Nuclei with A up to ≈ 60 are produced in these reactions. A relative drop of the abundance of the nuclei with A > 60 is an effect of Coulomb barriers. The reactions of the first group generate energy in the static period of the star evolution. As the temperature in the center of the star increases photodisintegration reactions begin to play more prominent role. These are the reactions producing lighter nuclei in disintegrations of nuclei by photons. Typical reactions of this group are (γ,n) and (γ,p). Photodisintegration reactions on medium nuclei 15 < A < 60 comprise the second group of the reactions and lead to production of protons and neutrons that interact with products of carbon and oxygen burning processes. As the reaction thresholds of Nα nuclei are higher than those of the neighboring nuclei they are less likely to be destroyed by photons and their relative abundance increases. This effect is observed for all 56 56 the α-particle formed nuclei up to the Ni isotope (T1/2 = 6.1 days). The Ni isotope is unstable and transmutes + 56 56 e 56 β 56 into Fe by two subsequent β-decays: 28Ni −→ 27Co −−→ 26Fe. Thus, at this stage of the stellar evolution processes of high-A nuclei production compete with photodisintegration processes. The α-particle capture reactions are in an equilibrium with reverse photodisintegration reactions, e.g.

28Si + 4He ↔ 32S + γ, (37)

32S + 4He ↔ 36Ar + γ. (38)

Figure 15 shows the chains of nuclear reactions leading to synthesis of elements from helium to germanium. For accurate calculations of nuclear abundances in stars, after the stages of oxygen, carbon, and silicon burning producing the iron group elements are terminated, experimental data on a large number of nuclear reactions in the upper left corner of Fig. 15 are needed starting from energies of several hundred keV.

FIG. 15: Chains of nuclear reactions leading to synthesis of elements from helium to germanium.

As an example Fig. 16 shows the most important photonuclear reactions (γ,p) and (γ,n) on the 28Si and 32S isotopes. Up to the mass numbers of A ≈ 60 the cross section values are more or less similar. Cross sections of the photoneutron reactions at energies below 30 MeV are known sufficiently well, but the cross sections of reactions with protons in final state were measured only at the energies 4—6 MeV greater than the reaction threshold. 19

FIG. 16: (γ,p) and (γ,n) reactions cross-sections on the 28Si and 32S isotopes.

IX. PHOTODISINTEGRATION OF THE IRON PEAK NUCLEI

If the initial mass of the star M > 10M , then the final stage of its evolution is a supernova explosion. The duration of the silicon burning stage is one day. Inside the silicon center of the star an iron kernel begins to form. At the border between the iron kernel and the silicon shell and outer layers synthesis of nuclei continues and energy is still being released. The central part, which consists of the iron group nuclei, begins to collapse. However, as the nuclear energy sources are exhausted (because the per nucleon binding energy of nuclei in the center of the star is at its maximum value), nuclear heating of the central part of the star stops and it is heated only by the gravitational energy, produced by collapsing. At the temperature of ∼ 5 · 109 K an important role begins to be played by reactions of breakup of the nuclei of the iron group into neutrons and α-particles 56Fe → 134He + 4n, Q = 124.4 MeV, (39) and reactions of weak interaction electron capture by free protons and nuclei, that lead to production of neutrinos: − − p + e → n + νe, (A, Z) + e → (A, Z − 1) + νe. (40) These reactions absorb energy and contribute to cooling down of the central part of the star. Figure 17 shows the main photonuclear reactions on the 56Fe and 63,65Cu isotopes belonging to the iron peak. Likewise to the light nuclei the cross sections at energies several MeV higher than the reaction thresholds are also unknown. Figure 18 shows a comparison of photoproton and photoneutron reaction cross sections on 58,60Ni. 20

FIG. 17: Main photonuclear reactions cross sections for 56Fe and 63,65Cu.

Figure 19 shows the dependence of integrated cross sections of the (γ,p) and (γ,n) reactions in the energy range of the GDR for the isotopes 52÷56Fe (Z = 26) on the mass number A as calculated by the combined model of the GDR. The results suggest a strong dependence of decay properties of the Fe isotopes on the thresholds of photonuclear reactions. The proton emission channel prevails for the neutron-deficient isotopes with A < 52. As the mass number A increases, the photoneutron channel becomes the dominant one. Far enough from the beta stability region for the neutron-rich iron isotopes with A > 60 the (γ,2n) channel of the GDR decay starts to play a prominent role. 21

FIG. 18: A comparison of photoproton (top) and photoneutron (bottom) reactions cross sections for 58Ni (left) and 60Ni (right) obtained using bremsstrahlung (dots) and quasimonoenergetic annihilation photons (line).

FIG. 19: Integrated cross sections of the (γ,n), (γ,2n), and (γ,p) reactions, as calculated for Fe isotopes for the energies of GDR using the combined model, versus the A-numbers. 22

X. p-NUCLEI

There are 35 isotopes from Sc (Z = 34) to Hg (Z = 80) in the neutron-deficient part of the beta stability valley, far away from the r- and s-process trajectories. The abundances of these nuclei are 2—3 orders of magnitude less than those of the neighboring nuclei produced in r- of s-processes. Selected trajectories of p-nuclei production are shown in Fig. 20. The isotopes 74Se, 78Kr, 84Sr, that are far from the s-process trajectories, are marked.

FIG. 20: A typical s-process diagram for the 72 ≤ A ≤ 89 region. Grey squares denote stable isotopes, white denotes unstable isotopes (half lives are shown). Circles mark the isotopes (74Se, 78Kr, 84Sr) produced in p-process, crosses mark the isotopes (82Se, 86Kr, 87Rb) produced solely in r-process.

The production of these nuclei, the so-called p-nuclei, can be explained under the assumption that they are produced in the following reactions [32]: 1. proton capture reactions (p,n), (p,γ); 2. photodisintegration reactions (γ,n), (γ,2n);

+ 3. weak interaction reactions e + (A, Z) → (A, Z + 1) +ν ¯e; 4. spallation reactions, where the incident accelerated protons and α-particles are produced during passage of shock wave through supernovae shells; 5. a mechanism of p-nuclei production by intense neutrino flux during supernova explosions was also suggested in a number of works:

∗ − νe + (A + 1,Z − 1) → (A + 1,Z) + e , (41)

(A + 1,Z)∗ → (A, Z) + n.

As a result of a neutrino capture and electron emission the (A + 1,Z) nucleus is produced in an excited state with the excitation energy being greater than the neutron separation energy of the (A + 1,Z) nucleus. Therefore, a decay of the excited (A + 1,Z) nucleus into (A, Z) with emission of a neutron is possible. Simulation of transformations of the s- and r-nuclides into p-nuclides requires processing of large-scale reaction chains involving more than ∼ 1000 nuclides from the iron peak region and more than ∼ 10000 reactions [32]. 23

Photodisintegration of Ta isotopes

180mTa is one of the nuclides produced in p-process. The 181Ta isotope comprises 99.988% of the natural tantalum. 180m P − Ta isotopes are peculiar for the longest known half life of the isomer Ta (J = 9 ,E = 75.3 keV, T1/2 = 1.2 · 1015 yr) state, comprising 0.012% of the natural isotope mixture. In the ground state the 180Ta isotope has a P + 180m half life of T1/2 = 8.152 h and J = 1 . The Ta isotope is blocked from the main trajectory of r- and s-processes by the stable 180Hf which is produced after a neutron capture. Therefore, natural 180mTa may be produced in the 181Ta(γ,n), 182Ta(γ,2n) reactions (Fig. 21).

FIG. 21: Diagram of the 180mTa p-nuclide production in the (n,γ), (γ,n), and (γ,2n) reactions. Stable isotopes are denoted with gray background, unstable—with white background (half lives are shown).

The p-process is essentially photodisintegrations, primarily of the (γ,n) kind. As the cross sections for processes of both ground and isomeric states production are of a great interest corresponding experiments were carried out previously using various photon sources: radioactive isotopes, bremsstrahlung, and quasimonoenergetic photons from positron annihilation in flight.

FIG. 22: Cross-section of the 181Ta(γ,sn) reaction. Curves: solid—combined model calculations [33], dashed—TALYS calcula- tion. Dots—experimental data: triangles—[34], empty circles—[35], squares—[36], dark circles—[37].

Figure 22 shows the 181Ta(γ,sn) reaction cross sections measured in experiments with quasimonochromatic photon beams and using the total absorption technique. The cross sections presented in the cited works significantly differ 24 from each other. However all works observe a splitting of the GDR into two maxima: one at the energy 12—13 MeV, the other at the energy 15—16 MeV. The splitting is due to deformed shape of the 181Ta nucleus. The value of the integrated cross section of the reaction calculated using the dipole sum rule is σirA = 60NZ/A = 2610 MeV·mb. The majority of the experimental results is in agreement with this estimate within 10% accuracy. The partial photonucleon reaction cross sections with 1—3 outgoing neutrons on the 181Ta isotope were measured using quasimonochromatic photon beams [35, 36]. A comparative analysis of the data was given in [15] and an evaluated cross section was obtained, which is shown in Fig. 22. In [38] photonucleon reactions cross sections were calculated using the combined model and the TALYS [39] package for the energies from reaction thresholds to 70 MeV for the 181Ta isotope. Integrated reaction cross sections of the reactions are shown in table II.

TABLE II: Integrated from Emin to Emax cross sections of photonucleon reactions on Ta. For each reaction integration limits Emin and Emax are shown Integrated cross section, mb E , E , Reaction min max CM [33] TALYS [39] [34] [36] [37] MeV MeV 181Ta(γ,n)180g.s.Ta 1730 1750 1300 1990 1580 7.58 18 181Ta(γ,n)180mTa 150 181Ta(γ,2n)179Ta 840 970 870 790 970 14.22 26 181Ta(γ,3n)178g.s.Ta 140 160 137 22.15 36 181Ta(γ,3n)178mTa 181Ta(γ,4n)177Ta 150 170 29.0 70 181Ta(γ,5n)176Ta 100 100 37.54 70 181Ta(γ,6n)175Ta 71 80 37.54 70 181Ta(γ,p)180g.s.Hf 5.1 39 5.94 70 181Ta(γ,p)180mHf 0.4 181Ta(γ,pn)179g.s.Hf 36 17 13.33 70 181Ta(γ,pn)179mHf

The most significant difference among the measured cross sections is observed for the 181Ta(γ,n) reaction. The total cross section of this reaction measured in [36] is 50% greater than the cross section measured in [35].The quasideuteron mechanism of photon absorption prevails in the energy range E > 40 MeV. Photonuclear reactions yields with 1 to 6 outgoing neutrons on the 181Ta isotope and isomer production in the reactions 181Ta(γ,p)180Hf and 181Ta(γ,np)179Hf were measured in [40]. Measured photonuclear reaction yields on the 181Ta isotope, normalized to the Ta(γ,n)Ta reaction yield are shown in table III.

TABLE III: Normalized yields of photonucleon reactions on the 181Ta nucleus. Spins and parities J P of the reaction products are shown. For 181Ta J P = 7/2+.

P Yield Y Reaction JF Experiment C.M. [33] TALYS [39] [35] [36] [41] 181Ta(γ,n)180g.s.Ta 1+ 1 0.93 1 1 1 1 181Ta(γ,n)180mTa 9− 0.07 181Ta(γ,2n)179Ta 7/2− 0.34 ± 0.07 0.29 0.32 0.42 0.24 0.37 181Ta(γ,3n)178g.s.Ta 1+ (1.8 ± 0.4) · 10−2 2.4 · 10−2 2.7 · 10−2 2 · 10−2 181Ta(γ,3n)178mTa 7− (5 ± 1) · 10−3 181Ta(γ,4n)177Ta 7/2+ (1.7 ± 0.5) · 10−2 1.0 · 10−2 1.1 · 10−2 181Ta(γ,5n)176Ta (1)− (5 ± 1) · 10−3 3.7 · 10−3 3.7 · 10−3 181Ta(γ,6n)175Ta 7/2+ (1.4 ± 0.3) · 10−3 1.2 · 10−3 1.3 · 10−3 181Ta(γ,7n)175Ta 3+ 6 · 10−5 6 · 10−5 181Ta(γ,p)180g.s.Hf 0+ 8 · 10−4 7 · 10−3 181Ta(γ,p)180mHf 8− (5 ± 1)·−4 3 · 10−5 181Ta(γ,pn)179g.s.Hf 9/2+ 5 · 10−3 1 · 10−3 181Ta(γ,pn)179mHf 25/2− (4 ± 3)·−5 25

The photoneutron cross section for 181Ta as a function of energy was measured using an LCS beam with high accuracy in the energy range of astrophysical relevance near the neutron threshold, which definitely revealed that existing database did not provide reliable (γ,n) cross sections [42]. The point is that LCS data are not consistent in the range of GDR with both well-known datasets obtained in Saclay and Livermore even if the latter is multiplied by a factor of 1.22 (according to the IAEA recommendations). Moreover Saclay data exhibit non-vanishing cross sections below (γ,n) threshold (7.58 MeV) energy (non-vanishing cross section could arise from subtracting a contribution of the positron bremsstrahlung involved into three-step technique of quasimonoenergetic photons production). The LCS experiment showed that in accordance with the Breit-Wigner theory the (γ,n) cross section near threshold can be expressed as σ = σ0[(E − 7.58)/7.58]p where σ0 = 207 mb and p = 0.96 (corresponds to l + 1/2 (if a single value of the neutron orbital angular momentum l contributes). Accurate cross section measurements showed that (γ,n) cross section behavior near the threshold is not described by a pure s-wave, but rather by a mixture of s- and p-waves. The mixed nature means that the photoneutron reaction 181Ta(γ,n)180Ta results (with l = 0 and 1) in decays to both 180g.s.Ta positive-parity (1+) ground state and 180mTa negative-parity (9−) isomeric excited state. To determine partial photoneutron cross section of the isomeric state 180mTa production measurements of total photoneutron cross sections σtot and partial cross sections σgs of the ground state production were performed using respectively direct neutron counting and photoactivation techniques. The ratios of total and ground state cross sections were obtained and used for determine the isomeric-state cross section. It was shown that weak partial cross section for the 9− isomeric state 180mTa is sensitive not only to the 181Ta E1 strength function, but also to the detailed level spectrum in 180Ta responsible for the E1 photon cascade down to the 9− isomeric state. Experimental studies of photonucleon reactions on 181Ta were performed using the aforementioned activation tech- nique. To compare the measured yield Y with the theoretically calculated yields the Ytheor yield was calculated as a convolution of the cross section σtheor(E) and the bremsstrahlung spectrum W (E,Emax):

E Zmax Ytheor(Emax) = σtheor(E)W (E,Emax)dE. (42) 0

FIG. 23: A comparison of experimental (solid line) and theoretical (combined model, dashes) 181Ta cross sections for reactions with different numbers of outgoing neutrons. The dotted line shows the quasideutron component contribution.

The yields of the 181Ta(γ,n) and 181Ta(γ,2n) reactions calculated from the cross sections measured in [35] and [36] are almost two times different. The experimental yields with 3 and more outgoing neutrons agree with the TALYS and CM calculations. A comparison of experimental and CM-calculated cross sections is shown in Fig. 23. 26

In [42] photoproton reactions with production of isomeric states 181Ta(γ,p)180mHf and181Ta(γ,np)179mHf were measured. The measured yields of the 181Ta(γ,p)180mHf and181Ta(γ,np)179mHf reactions are approximately 100 and 10 times less than the respective yields of the reactions 181Ta(γ,p)180Hf and181Ta(γ,np)179Hf calculated in the frame of the combined model. This is not unexpected as it should be taken into consideration when comparing the experimental results with the calculations that small isomeric yields are due to a large difference between the spins of the initial 181Ta nucleus (J P = 7/2+) and the final nuclei 180mHf (J P = 8−) and 179mHf (J P = 25/2−). For heavy nuclei the difference between the ground and isomeric state production yields should be approximately the same at such a large value of spin difference. Isospin splitting of the GDR [40] is not accounted for in TALYS and the photoproton reactions cross sections calculated by this program for heavy nuclei are 2—3 orders of magnitude less. The CM doesn’t calculate the isomeric production channel. Comparison of the yields of the 181Ta(γ,n)180mTa reaction to the concentration of 181Ta and 180Ta in natural tantalum suggests that the (γ,n) reaction on the 181Ta isotope is one of the main mechanisms of the 180mTa p-nuclide production. Another possible mechanism of 180mTa production could be the neutrino induced reaction on the 180Hf isotope

180 180m − νe + Hf → Ta + e . (43)

Another possible channel of the 180mTa production in s-process was studied in [43]. Neutron capture by a 179Ta nucleus can produce a 180mTa nucleus. However, it is preliminary now to make realistic estimates and to choose among the discussed 180mTa production options, as the cross sections of the reactions taking part in its production are not known to a sufficient accuracy.

Photodisintegration of Hg isotopes

The experimental data available on the Hg photodisintegration is extremely scarce. In [44] cross sections of the photoneutron reactions (γ,n) and (γ,2n) on natural Hg were measured. In [45] the yield and cross section of the photoproton reaction on the 201Hg isotope were obtained. In [46] yields of several photonuclear reactions on stable Hg isotopes were measured using bremsstrahlung beams with end-point energies of 19.5 and 29.1 MeV. In [46] total photoabsorbtion cross sections σ(γ,abs), partial photoneutron σ(γ,n), σ(γ,2n), photoproton σ(γ,p) and σ(γ,n+p) cross sections were calculated based on the combined model [33]. In Fig. 24 calculated (γ,n) and (γ,2n) reactions cross sections on natural Hg are compared with the experimental data from [44]. The photoneutron cross sections are described by the model with a good accuracy as it follows from the comparison.

FIG. 24: Cross-sections of partial photonuclear reactions on natural Hg. Curves: solid—calculated (γ,n) reaction cross- section, dotted—calculated (γ,2n) reaction cross-section. Dots [44]: empty circles—(γ,n) reaction cross-section, triangles— (γ,2n) reaction cross-section. 27

For the Hg isotopes (Fig. 25) the N and Z numbers are close to magic, and the shape of the nucleus is close to a sphere, so the giant resonance shows itself as a single rather narrow maximum with the width Γdip ≈ 4.2—4.6 MeV. The width of the cross section on the Hg isotopes is the same as the width of the photoabsorbtion cross section on the doubly magic 208Pb nucleus (Z = 82,N = 126) [47].

FIG. 25: Diagram of the Hg isotopes production in the (n,γ), (γ,n), (γ,2n), and (γ,3n) reactions. Stable isotopes are denoted with gray background, unstable—with white background (half lives are shown).

The calculated total cross-sections of the (γ,n), (γ,2n), and (γ,p) reactions for different Hg isotopes are shown in Fig. 26.

FIG. 26: CM-calculated integrated photonucleon reaction cross-sections on stable Hg isotopes. Dots: triangles—(γ,n), empty circles—(γ,2n), crosses—(γ,p). The total cross-section (γ,p) is shown scaled up 15 times for clarity.

Total photoabsorbtion cross sections vary slightly as the mass number A changes from σint(γ, abs) ≈ σint(γ, n) + 196 σint(γ, 2n) + σint(γ, p) = 3421 MeV · mb for the lightest Hg isotope to σint(γ, abs) = 3580 MeV · mb for the heaviest 204Hg isotope which is in agreement with the value of the total cross-section calculated from the dipole sum rule. The GDR state decays mainly with emission of a single neutron. The σ(γ, n) reaction cross sections generally decrease as the mass number A increases, but still comprise the main part (65—75%) of the total photoabsorbtion cross section. The maximum of the σ(γ, n) reaction cross section is at the same energy as the GDR maximum for all stable Hg isotopes. 28

The σ(γ, 2n) reaction cross sections increase as the mass number A increases from 606 MeV · mb (196Hg) to 907 MeV · mb (204Hg) which is explained by the shift of the σ(γ, 2n) reaction threshold in the direction of GDR maximum resulting in an increased probability of GDR decay with two outgoing neutrons. For the 204Hg isotope the σ(γ, 2n) reaction threshold is at the same energy as the GDR maximum. By folding the calculated cross sections [48] with a bremsstrahlung spectrum the yields of the photonuclear reactions on Hg isotopes were obtained at two bremsstrahlung end-point energies: E = 19.5 and 29.1 MeV. A comparison with the experimentally measured yields is given in table IV. The comparison shows that the mechanism of photon interaction and GDR decay for the Hg isotopes is generally well described by the combined model [48].

TABLE IV: Measured and calculated using the combined model photonuclear reaction yields on stable Hg isotopes. The yields are normalized to the 196Hg(γ,n)195Hg reaction yield.

The yields of the (γ,n) reactions are equal to the calculation results within experimental errors at both energies E = 19.5 and 29.1 MeV. In [47] the isomeric state E∗ = 298.93 keV, J P = 13/2+ in the 197Hg isotope and E∗ = 532.48 keV, J = 13/2+ in the 195Hg isotope yields were measured for the first time. Isomeric yields in the 197Hg and 195Hg isotopes are almost equal within the accuracy of the experiment for E = 19.5 and 29.1 MeV. In both cases the isomeric state yield is several percent of the ground state yield. Such a difference is due to a large spin difference of the ground and isomeric states (table IV). The photoproton reactions yields on the 199,200,201Hg isotopes were measured in [49] (table IV). The yields of photoproton reactions on the 199,200,201Hg isotopes are respectively 3.9 · 10−4, 4.6 · 10−4, and 2.3 · 10−4, which is about 10−4 of the photoneutron reactions yield. The photoproton reactions yields at E = 29.1 MeV are by an order of magnitude greater than the yields of corresponding reactions at E = 19.5 MeV, which can be explained by the shift of the maximum of the cross section of the photoproton reaction into the energy range > 20 MeV due to isospin splitting and T> states excitation [49]. A similar situation can be seen in the theoretical calculations: as the upper energy of the bremsstrahlung spectrum increases from E = 19.5 to 29.1 MeV the yields of the photoproton reactions increase by an order of magnitude. The total photoproton reaction cross section increases due to: • decreasing of the photoproton reactions threshold as the mass number A decreases; • decreasing of the nuclear potential barrier as the distance to the beta stability band increases. At the same time it should be noted that the experimental photoproton yields are systematically 2—4 times greater than the calculation. The stable 196Hg isotope is a p-nuclide as is it separated from the sequence of nuclei produced in r- and s-processes by short-lived 147Hg and 196Au isotopes. A possibility of 196Hg production in the 198Hg(γ,2n)196Hg reaction was experimentally concerned in [49]. The end-point energy of the bremsstrahlung radiation varied from 18 to 30 MeV. Despite the approximate nature of the calculations where a number of specific astrophysical effects is not taken into account they show that the 196Hg production in the 198Hg(γ,2n)196Hg reaction is sufficient to explain the observed abundances of this isotope by its production in photonuclear reactions. 29

XI. PHOTOFISSION

It is well-known that many nuclei heavier than iron are produced in r-process. This is especially true for the nuclei heavier than Bi. r-process requires high temperature T > 2 · 109 K and neutron concentration n > 1019 cm−3. The r-process is limited by nuclear fission. The fission rate exceeds the beta decay rate for the nuclei with mass number A > 210. The 204,206,207,208Pb and 209Bi isotopes are the heaviest stable isotopes produced in s-process. An important role for the nuclei with Z > 83 is played also by α-decay. As it was shown above, it is not possible to get to the region of higher Z values through a sequence of transformations by beta decay

− 209 210 β 210 α 206 83 Bi + n → 83 Bi −−→ 84 Po −→ 82 Pb. (44)

232 234,235,238 At the same time the isotopes 90 Th and 92 U, which are naturally abundant, are produced in r-process. Intense neutron and photon fluxes induce fission reaction in U and Th producing a broad range of nuclides—fission fragments. The total cross section of uranium photodisintegration in the energy range of the giant dipole resonance is composed of the cross sections of the photoneutron reactions with one or two outgoing neutrons σ(γ, n) and σ(γ, 2n) and total photofission cross section σ(γ, F ).

σ(γ, tot) = σ(γ, n) + σ(γ, 2n) + σ(γ, F ). (45)

In the energy range below 20 MeV the photoneutron reaction cross sections were measured in several experiments. Figure 27 shows the photonuclear reaction cross-sections measured using quasimonochromatic photon beam. There are two maxima in the total photoabsorbtion cross section σ(γ, tot) at the energies E(1) = 10.77 MeV and E(2) = 13.80 MeV, which are a result of a deformed shape of the 238U nucleus in the ground state. The first maximum reveals itself in the main reaction channel (γ, n), the second one—in the (γ, 2n) reaction channel. The (γ, n) and (γ, 2n) were separated based on analysis of energy spectra of slowed-down neutrons at different distances from the studied target using coincidence setup. There are two different channels of 238U fission: • (γ, fiss)—fission into two fragments from an excited state of the 238U nucleus; • (γ, n fiss)—fission into two fragments from an excited state of the 237U nucleus produced after emission of a neutron.

σ(γ, F ) = σ(γ, fiss) + σ(γ, n fiss). (46)

Fission produces a broad spectrum of fragment masses in the mass range A = 85—150. Mass distributions of photofission fragments at different end-point energies of the bremsstrahlung spectrum are shown in Fig. 28. Photofis- sion produces approximately 80 different chains of unstable isotopes. There are two maxima in the mass distribution, corresponding to the mass numbers A = 94—101 and A = 133—141. As the energy of the bremsstrahlung beam 238 237 increases the value of Yγ,F /Yγ,n—the ratio of the photofission channel to the U(γ,n) U reaction channel—also increases. As the upper energy of the bremsstrahlung spectrum increases the fissibility of a nucleus—the ratio of the photofission cross-section to the total cross-section—also increases. 30

600 a 500

400

300

200 Cross section, mb 100

0 4 6 8 10 12 14 16 18 20 Energy, MeV 400

350 b

300

250

200

150

Cross section, mb 100

50

0 4 6 8 10 12 14 16 18 20 Energy, MeV 300 c 250

200

150

100 Cross section, mb 50

0 4 6 8 10 12 14 16 18 20 Energy, MeV 180 160 d 140 120 100 80 60 Cross section, mb 40 20 FIG. 28: Mass distributions of fission fragments pro- 0 duced at different upper energies of the bremsstrahlung 4 6 8 10 12 14 16 18 20 spectrum: (a)—T = 19.5 MeV, (b)—T = 29.1 MeV, Energy, MeV (c)—T = 48.3 MeV, (d)—T = 67.7 MeV [51]. The photofission reaction yield is normalized to the yield of FIG. 27: Cross-sections of photonuclear reactions on the 238U(γ,n)237U reaction. the 238U nucleus: (a)—(γ, tot), (b)—(γ, n), (c)—(γ, 2n), (d)—(γ, F ). Data from [50]. 31

Conclusions

Experimental data for the cross sections of photonuclear reactions measured experimentally typically have accuracy of about 10%. There are significant disagreements in data among various channels, especially for photoneutron reactions, which are studied more thoroughly than reactions with emission of charged particles. For astrophysics there is an additional difficulty coming from a definite lack of data at the energies near the nucleon separation threshold. Further developments of theory, models, evaluations, and experimental methods in the field of photonuclear in- teractions are required in order to obtain a more accurate description of the astrophysical processes involving such reactions. Results of the first studies in nuclear physics had shown that nuclei contain an enormous energy that can be the source of energy of stars. Stars do not only consume nuclear energy but are also the place where the nuclei, not present at the initial stage of the Universe, are produced. Constant evolution of astronomical, satellite-based observations, as well as of methods of nuclear physics, allow to penetrate more deeply into the secrets of the Universe. Discovery of the Dark mater, accelerated inflation of the Universe are a strong argument for necessity of further development of methods and increase in accuracy in the field of nuclear astrophysics.

Acknowledgments

Authors are indebted to Drs. S. S. Belyshev, V. A. Chetvertkova, and A. A. Kuznetsov for help in obtaining and analyzing the data and to the accelerator group—Prof. V. I. Shvedunov, Drs. A. N. Ermakov and V. V. Khankin—for providing support during experimental studies.

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