Cross sections for production of 43Sc, 44Sc, and 46Sc isotopes in the 45Sc + 3He reaction

Reactions ⁴⁵Sc(³He, αn)⁴³Sc, ⁴⁵Sc(³He, α)⁴⁴Sc, and ⁴⁵Sc(³He, 2p)⁴⁶Sc, resulting from the irradiation of scandium targets with a beam of ³He ions with energy from 5 to 24 MeV, are investigated in experiments on the U120M cyclotron of the Nuclear Physics Institute (Rez, Czech Republic). The activation technique is used to find the yield of the produced Sc isotopes. The induced γ activity in the targets is measured using a high-resolution HPGe detector. Despite the low binding energy of ³He and positive reaction Q values, which leads to formation of the ⁴⁴Sc and ⁴⁶Sc isotopes, the behavior of the excitation functions for the formation of these isotopes differs from the behavior of the excitation function for deuterons. Scandium-44 formation cross sections reach their maximum at the reaction Coulomb barrier. This is because not only ⁴⁴Sc but also a stable ⁴He nucleus is formed in the reaction.     

Excitation functions for 44Sc, 46Sc, and 47Sc radionuclides produced in the interaction of 45Sc with deuterons and 6He

Experimental excitation functions are presented for ⁴⁵Sc(d, p)⁴⁶Sc, ⁴⁵Sc(d, t)⁴⁴Sc, ⁴⁵Sc(⁶He, ⁵He*)⁴⁶Sc and ⁴⁵Sc(6He, α)⁴⁷Sc reactions at projectile energies near the Coulomb barrier. The obtained excitation functions for reactions ⁴⁵Sc(d, p)⁴⁶Sc and ⁴⁵Sc(⁶He, ⁵He*)⁴⁶Sc have similar behavior and have a maxima near the Coulomb barriers of these reactions. The compilation of the available experimental data, obtained at deuteron- and ⁶He-energies near the Coulomb barrier, showed that the values of the cross sections at the maxima of the excitation functions obtained in (d, p) reactions and the reactions for one-neutron pickup from the ⁶He projectiles have a different Z-dependence.     

Near-barrier neutron transfer in reactions <Superscript>6</Superscript>He + <Superscript>45</Superscript>Sc, <Superscript>64</Superscript>Zn,and <Superscript>197</Superscript>Au

Experimental cross sections of formation of isotopes ⁴⁶Sc (in reaction ⁶He + ⁴⁵Sc), ^196,198Au (in reaction ⁶He + ¹⁹⁷Au), and ⁶⁵Zn (in reaction ⁶He + ⁶⁴Zn) are analyzed. The time-dependent Schrödinger equation for the outer neutrons of ⁶He and ¹⁹⁷Au nuclei is solved numerically to calculate the probability of neutron transfer and transfer cross sections. In reaction ⁶He + ¹⁹⁷Au, the contribution of fusion and subsequent evaporation to experimental data can be neglected, while the corresponding contributions to reactions ⁶He + ⁴⁵Sc and ⁶He + ⁶⁴Zn are considerable. Fusion–evaporation is taken into account using the computational code of the NRV knowledge base. The results of calculations are in satisfactory agreement with the experimental data.     

Near-barrier neutron transfer in reactions with <Superscript>3</Superscript>He nucleus

Experimental cross sections for the formation of ^196,198Au isotopes in the ³He + ¹⁹⁷Au reaction and ^44,46Sc isotopes in the ³He + ⁴⁵Sc reaction are analyzed. To calculate transfer probabilities and cross sections, the time-dependent Schrödinger equation is numerically solved for the external neutrons of the ³He, ⁴⁵Sc, and ¹⁹⁷Au nuclei. It is shown that the contribution from the fusion channel with subsequent evaporation is important for the ³He + ⁴⁵Sc reaction and negligibly small for the ³He + ¹⁹⁷Au reaction. Fusion–evaporation is taken into account using the NRV and PACE codes. Calculation results demonstrate overall satisfactory agreement with experimental data.     

Cross sections and thermonuclear reaction rates for 42Ca(p, γ)43Sc, 44Ca(p, γ) 45Sc, 44Ca(p,n) 44Sc and 45Sc(p,n)45Ti

The yield of γ-rays from the reaction ⁴²Ca(p, γ)⁴³Sc has been measured as a function of bombarding energy over the range 0.63–3.01 MeV, from ⁴⁴Ca(p, γ)⁴⁵Sc over the range 0.775–4.00 MeV, from ⁴²Ca(p, p'γ)⁴²Ca over the range 2.24–3.01 MeV, and from ⁴⁴Ca(p, p'γ)⁴⁴Ca over the range 1.90–5.03 MeV. The cross section of the reaction ⁴⁴Ca(p, n)⁴⁴Sc has been measured from threshold to a bombarding energy of 5.05 MeV by observation of the 1157 keV γ-ray associated with the residual ⁴⁴Sc activity, and the cross section of the reaction ⁴⁵Sc(p, n)⁴⁵Ti has been measured from threshold to a bombarding energy of 4.00 MeV both by observation of the annihilation radiation associated with the residual ⁴⁵Ti activity and by measurement of the total neutron yield with a wide-angle BF₃ tube and paraffin detector. All these data are compared with statisticalmodel calculations and satisfactory agreement is achieved. Thermonuclear reaction rates for the (p, γ) and (p, n) reactions are calculated for the temperature range 5 × 10⁸-10¹⁰K and the significance of these results for explosive nucleosynthesis in stars is discussed.     

The45Sc(3He,d)46Ti reaction. DWBA analysis of transitions to states between 7.6 and 11.0 MeV

Angular distributions of transitions to 29 states in⁴⁶Ti between 7.6 and 11.0 MeV excitation energy from the⁴⁵Sc (³He,d) reaction at 15 MeV have been compared with DWBA predictions. The results support previously suggestedT=2 states in⁴⁶Ti.     

Near-Barrier Proton Transfer in Reactions with <Superscript>3</Superscript>He Nucleus

Calculations of production cross sections for isotopes ¹⁹⁴Au in the ³He + ¹⁹⁴Pt reaction and ⁴⁵Ti in the ³He + ⁴⁵Sc reaction are performed, based on the solution to a time-dependent Schrödinger equation in combination with calculations in the statistical model using the computational code of the NRV data base. The experimental differences in the near-barrier energy dependences of the isotope production cross sections in these reactions are explained by the difference between the proton and neutron shells of the target nuclei, and by the different evolutions of the probability density for protons of the projectile nucleus and neutrons of the target nuclei in collisions.     

Investigating the nuclear fusion and nucleon transfer channels in the 197Au + 6He reaction at 6He energies up to 20 MeV/A

New data on the cross sections of reactions that proceed during the interaction of ⁶He and ¹⁹⁷Au nuclei in the ⁶He energy range of 40 to 120 MeV are reported. The experiments were performed using the secondary beam of the ACCULINNA separator at the Flerov Laboratory of Nuclear Reactions (FLNR), JINR. Reaction products are identified by means of activation method to measure the gamma activity of a thin-foil target assembly. Excitation functions for ⁶He fusion reactions with subsequent emission of up to 10 neutrons from the compound nucleus are measured. Cross sections for reactions with emission of charged particles and nucleon transfer were also measured. The experimental cross sections for the (⁶He, xn) reactions that proceed via the formation of a compound nucleus agree in general with calculations using models that involve the statistical approach. It is shown that the complete fusion reaction cross section drops slightly up to an energy of 114 MeV. The experimental excitation functions for the reactions resulting in the formation of mercury and gold isotopes indicate that the main contribution to their formation comes from direct processes, while the evaporation reactions (⁶He, pxn) and (⁶He, αxn) are of minor importance.     

The46Ti(d,τ)45Sc reaction

The⁴⁶Ti(d, τ)⁴⁵Sc reaction has been investigated at an incident energy of 52 MeV. Angular distributions have been taken for 14 τ-groups corresponding to excitation energies below 4 MeV in⁴⁵Sc. Spectroscopic factors were extracted through DWBA calculations. Spins and parities of 5/2⁺ are proposed for states at 1.30, 1.80, 2.91, 3.48, and 3.72 MeV. The hole state spectrum of⁴⁵Sc closely resembles that of⁴⁷Sc. A strong fractionation of the 1d _3/2 strength was not observed in contrast to other recent work. The data provide evidence for (1f _7/2 · 1f _5/2 ¹) components in the ground state wave function of⁴⁶Ti, which demonstrates that such configurations are not restricted to neutron excitations.     

Isomeric cross sections for the (n, 2n) reaction on 82Se, 81Br,and 45Sc at 15.1 MeV

Activation techniques have been used to measure the cross sections at 15.1 MeV neutron energy for the following reactions: ⁸²Se(n, 2n)^81m+gSe, ⁸¹Br(n, 2n)^80m+gBr, and ⁴⁵Sc(n, 2n) ^44m+gSc. Isomeric cross-section ratios were evaluated by applying the method of least squares to the time behavior of γ-ray activity following the ground-state decay of each isomeric pair. The absolute cross section σ_m for the formation of the metastable state was measured by the mixed-powder method with the ²⁷Al(n, α)²⁴Na reaction as the monitor. The cross section σ_g for the formation of the ground state was then determined by using the isomeric cross-section ratio. The sum of σ_m and σ_g for each reaction is compared with the theoretical value obtained from calculations based on the statistical model for the formation of a compound nucleus and its subsequent emission of neutrons.     

Compound nucleus contribution and even-odd effect for (3He,p) reactions in the Ni region

The compound nucleus contributions to the proton spectra from 8 MeV and 10 MeV ³He induced (³He, p) reactions on even-A Ni isotopes were obtained. The relative cross sections for ⁵⁸Ni/⁶⁰Ni/⁶²Ni in the high excitation region are in fair agreement with predictions of statistical theory, but the absolute cross sections in the same region are smaller than the prediction by a factor of 3 to 8, and the shapes of the measured spectra for heavier isotopes do not agree with the prediction. These discrepancies between experiment and theory are in sharp contrast to the situation in (p, p′), (p, α), (α, p) and (α, α′), where good agreement was found.The proton spectra from (³He, p) reactions on nuclei in the A = 54–68 mass range have a systematic difference in slope between even-A targets and odd-A targets; it is similar to the systematic difference found previously in (p, p′) and (α, p) reactions, but none of these is readily explainable by theory.     

Single-particle and core-excited states in 49Sc: (II). The 48Ca(α, t)49Sc reaction

The ⁴⁸Ca(α, t)⁴⁹Sc reaction has been studied at 36 MeV incident energy. About eighty levels have been observed up to 7.5 MeV excitation energy and angular distributions were measured from 6° to 58°, using a split-pole spectrometer. A local zero-range DWBA analysis has been carried out, and the deduced l-assignments and spectroscopic factors are compared with those obtained from the (³He, d) reaction. In the other hand, a large number of angular distributions cannot be reproduced by the DWBA calculations; they have been compared with the results of coupled-reaction-channel calculations, assuming two-step excitation of weak coupling states with a [${}^{48}\text{Ca}{}^1\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$] structure. Good agreement between experimental angular distributions and two-step predictions is obtained for several ⁴⁹Sc levels, suggesting spin and parity assignments. Moreover, as rather large cross sections are predicted for two-step excitations, it is concluded that, generally, these processes cannot be neglected in the analysis of (α, t) reactions.     

Study of fusion and nucleon transfer channels in the <Superscript>197</Superscript>Au + <Superscript>6</Superscript>He reaction in an energy range of <Superscript>6</Superscript>He to 20 Mev/A

New data on the cross sections of reactions occurring during the interaction of ⁶He nuclei with ¹⁹⁷Au at energies of ⁶He from 40 to 120 MeV are presented. The experiments were performed in the ACCULINNA secondary beam separator of the Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. To identify the reaction products, the activation method for measuring the gamma activity of the target assembly of thin foils was used. The excitation functions for fusion reactions involving the evaporation of up to ten neutrons from the compound nucleus as well as reactions with the emission of charged particles and nucleon transfer in the investigated energy region are obtained. Data analysis was carried out using two codes: ALICE-MP and NRV. The cross sections for the (⁶He, xn) reactions occurring through the compound nucleus are mostly in agreement with the results of model calculations based on the statistical approach. It is shown that, up to the energies of 114 MeV, the cross-section drop in the complete fusion reactions is negligible. The experimental excitation functions of reactions leading to the formation of isotopes of mercury and gold (transfer reaction) indicate that the main contribution to their formation is made by direct processes and that evaporation reactions (⁶He, pxn) and (⁶He, αxn) play a minor role, as is evidenced by a comparison of the measured cross sections with the calculation results.     

Fusion excitation functions near and below the Coulomb barrier for symmetric and asymmetric medium-mass systems

Fusion excitation functions for the systems ¹²C + ^{46, 48, 50}Ti, ^{28, 30}Si + ³⁰Si and ¹⁸O + ⁴⁴Ca have been determined at energies near and below the Coulomb barrier. Inelastic excitation functions for the targets ^{48, 50}Ti and ⁴⁴Ca have been also measured in the same energy range. The absolute cross sections were obtained by in-beam γ-ray spectroscopy technique using a rotating target. Fusion cross sections ranging in magnitude from ～ 0.3 mb to ～ 1300 mb were determined with an accuracy of 10–20%. The fusion excitation functions are analysed in the frame of a semiclassical barrier-penetration model. From the analysis, the height, the radius and the curvature of the fusion barrier for the different systems are extracted. The fusion cross sections are compared with the calculations performed using different heavy-ion potentials. The enhancement of the cross sections at sub-Coulomb energies can be reproduced with a one-dimensional barrier-penetration model taking into account the zero-point motion of the surface of the reaction partners. The fusion cross section of the system ¹⁸O + ⁴⁴Ca is well reproduced by quantum-mechanical calculations, introducing a new degree of freedom taking into account the formation of a neck during the fusion process.     

Cross sections and isomeric ratios in the photoproduction of 44Sc from heavier nuclei

The yields and isomeric yield ratios in the photoproduction of⁴⁴Sc from ⁴⁵Sc, ⁵⁵Mn, Fe, ⁵⁹Co and ⁷⁵As have been measured by activation methods in the energy region 100–800 MeV. Mean cross sections and isomeric cross-section ratios in the energy region 250–800 MeV have been deduced and the number of valence neutrons available for the (γ, n) reaction estimated. The experimental cross sections are compared both to cascade-evaporation calculations based upon the free-nucleon photopion cross sections and to cross sections calculated with a semi-empirical formula. The isomeric cross-section ratios are compared to calculations based on the statistical formalism by Huizenga and Vandenbosch together with cascade-evaporation theory.     

Hyperfine anomalies of Sc isotopes (A = 44, 44 m, 46 and 47) in iron

Nuclear magnetic resonance on oriented nuclei (NMR-ON) on Sc isotopes (A = 44, 44 m, 46, 47) in Fe were performed. Using the known magnetic moments the magnetic hyperfine fields were determined. The hyperfine anomalies of various Sc were deduced; ⁴⁴Δ⁴⁷ = 0.0 (12) %, ^44mΔ⁴⁷ = 1.2 (4) %, ⁴⁶Δ⁴⁷ = 2.7 (8) %. The measured hyperfine anomalies are briefly discussed based on the shell model.     

Excitation functions of some neutron threshold reactions on isotopes of molybdenum

Cross sections were measured for (n,p) reactions on ^{92, 95, 96, 97, 98}mo, (n, α) reactions on ^{92, 98}Mo, and (n, 2n) reaction on ¹⁰⁰Mo for the first time in the neutron energy range of 5.9 to 9.6 MeV. The quasi-monoenergetic neutrons were produced via the ²H(d, n)³He reaction using a deuterium gas target at a compact cyclotron. Use was made of the activation technique in combination with high-resolution γ-ray spectroscopy. Some systematic trends observed in the excitation functions are discussed. For the various isotopes of molybdenum, with increasing mass of the target nucleus, the thresholds of (n,p) and (n,α) reactions increase and the magnitudes of cross sections near the maxima of the excitation functions appear to decrease. Hauser-Feshbach calculations show that in general the excitation functions of (n, p) and (n, α) reactions are described within a factor of 2 by the statistical model only up to about 8 MeV; the (n,2n) reaction on ¹⁰⁰Mo, however, is reproduced well from threshold up to 15 MeV by this model.     

Low-energy proton reactions on 45Sc of interest in stellar nucleosynthesis

Differential cross sections on ⁴⁵Sc have been measured for inelastic scattering (p, p_i; i = 2–13) at lab angles of 70° and 110° in the proton energy range 2.5 to 3.5 MeV and for the (p, α_{0, 1}) reactions at 125° between 2.8 and 3.8 MeV. Angular distributions were obtained at incident energies of 2.90, 3.15 and 3.40 MeV. These data were compared with calculations performed with a Hauser-Feshbach statistical model and average parameters which have been used to calculate reaction rates during stellar nucleosynthesis. The general agreement between the calculations and the trend of the data supports the use of these calculations for reaction rates involving nuclei in excited states, a situation important during stellar silicon burning.     

Nuclear structure of 47Sc: (I). Gamma-ray correlations and lifetime measurements

Levels of ⁴⁷Sc below an excitation energy of 2.7 MeV have been investigated through the ⁴⁴Ca(α, pγ)⁴⁷Sc reaction. Gamma-ray spectra in coincidence with protons were recorded with a Ge(Li) detector positioned at several angles and at α-energies of 10.15 and 11.00 MeV. Level positions, lifetimes, decay modes and spin values were deduced from these measurements. This study was supplemented by a γ-γ coincidence measurement. The electromagnetic properties for the negative parity states are compared with intermediate coupling predictions. A classification of the positive parity states into several rotational bands is proposed.     

The structure and properties of45Sc at low excitation energies

The spins and electromagnetic properties of levels in⁴⁵Sc up to 2,352 keV were studied by means of inelastic proton scattering using a 3-parameter coincidence arrangement and Coulomb excitation with³He and⁴He beams. Relevant experimental results are discussed in terms of the Thankappen-True core-plus-particle model.