The (τ,d), (d,p) and (d,n) reactions on28Si

The model of a three-particle proton cluster coupled to the quadrupole vibrational field is applied to¹²⁹I. The energy spectrum and spectroscopic factors, as obtained in a (³He,d) stripping reaction, are calculated and compared with experimental data. With the wave functions obtained magnetic-dipole and electric-quadrupole moments are derived.     

O(d,d) symmetry in quantum cosmology

We analyze the quantum cosmology of one-loop string effective models which exhibit an O(d, d) symmetry. It is shown that due to the large symmetry of these models the Wheeler-de Witt equation can completely be solved. As a result, we find a basis of solutions with well-defined transformation properties under O(d, d) and under scale factor duality in particular. The general results are explicitly applied to 2-dimensional target spaces while some aspects of higher dimensional cases are also discussed. Moreover, a semiclassical wave function for the 2-dimensional black hole is constructed as a superposition of our basis.     

Be9(d,p),(d,t),(d,a)反应研究

本文在E_d=0.1—2.5MeV能量范围内,研究了Be⁹(d,p₀)Be¹⁰(0),Be⁹(d,p₁)Be¹⁰(3.368MeV),Be⁹(d,t₀)Be⁸(0),Be⁹(d,α₀)Li⁷(0)及Be⁹(d,α₁)Li⁷(0.478MeV)诸反应。在E_d=0.150,0.220,0.401,0.706,1.005,1.301,1.484,1.750,2.000,2.250和2.500MeV共十一个能量上分别测量了这五群出射粒子在θ_L=10—155°区间的角分布。在θ_L=135°,E_d=0.1—2.5MeV,在θ_L=95°,E_d=0.1—2.2MeV,和在θ_L=112.5°,E_d=0.5—2.5MeV测量了Be⁹(d,p₀)Be¹⁰的激发函数。在θ_L=135°和112.5°,E_d=1.2MeV,用较厚靶(100—300μg/cm²)测量了Be⁹(d,p₀)Be¹⁰(0)反应的截面绝对值,结果为σ_(p0)(θ_L=135°)=1.60mb/sr,σ_(p0)(θ_L=112.5°)=1.55mb/sr。这样就得到了在此能区内,这五群出射粒子的截面情况。对所得结果进行了一些讨论。     

The Zr(d,n)Nb and Zr(d,n)Nb reactions

The (d, n) reaction on ⁹⁰Zr and ⁹⁶Zr has been studied at 12 MeV deuteron bombarding energy using the neutron time-of-flight technique with an overall neutron time resolution of 1.9 ns. Angular distributions of neutron groups leading to states in ⁹¹Nb and ⁹⁷Nb were measured in the angular range between 15° and 60°. The measured cross sections were analyzed in the framework of the distorted-wave theory of stripping reactions to deduce l-values and proton spectroscopic factors of states in the residual nuclei. The results are compared with the corresponding data available from (³He, d) studies. The fractionation of the single-particle proton states and their centroid energies are determined.     

Statistical analysis of the (d,p) and (d,d) reactions on 40Ca

Excitation functions of the ⁴⁰Ca(d, p)⁴¹Ca and ⁴⁰Ca(d, d)⁴⁰Ca reactions have been measured at 45°, 90°, 135° and 170° from E_d = 4.50 to 5.43 MeV in 10 keV steps. Angular distributions of these reactions have been taken at E_d = 4.70, 5.00 and 5.30 MeV from 25° to 170° in 5° steps. Transitions were observed to the excited states for the range 0.0 ≦ E_x ≦ 3.74 MeV in ⁴¹Ca. Rapid fluctuations in the excitation functions and strong variations of the angular distributions with the incident energy were observed, suggesting that the contribution from compound nucleus processes is very large. Various quantities extracted from the experimental data were compared to the predictions of the statistical theories combined with the DWBA theory for the calculation of the direct reaction amplitudes. The results of the present analysis are consistent with the predictions of the standard statistical theories based on the neglect of the channel-channel correlation.     

(π, d) Pick-up reaction

The reaction π + A → d + B at low energy is studied in a one-step DWBA framework. The nuclear structure aspects of the reaction are investigated. The reaction involves mostly neutron or proton pairs of the target nucleus with large total momentum and with total spin equal to zero. In the case of even-even nuclei with a partially filled shell, the coherence of the contributions from different orbitals produces an enhancement of the ground state to ground state transitions. Distortion effects are found to be very large. The final-state interaction is crucial in bringing the magnitude of the differential cross section into satisfactory agreement with the experimental value.     

The Estimation of the Difference Between d(d,n)3He and d(d,p)T Cross Sections in the Cold Fusion

The difference between two reaction cross sections of d(d, p)T and d(d, n)³He has been estimated in the cold fusion. It is caused by the different potential wall transmission and the angular distribution due to the structure.of deuterons. The rough estimation indicates that the branching ratio b about two orders of magnitude.     

Topologically Stable Lumps in SO(d) Gauged O((d+1) Sigma Models in d Dimensions: d =2,3,4

The gauge-invariant topological charge is defined for, and the inequalities supplying the lower bound on the action of an SO(4) gauged O(5) sigma model in four dimensions are established. The consistency of the solution with finiteness of the action and with topological stability is briefly verified for a particular dynamical example. Against the background of the topologically stable finite energy solitons of SO(d) gauged O(d+1) sigma models in d dimensions already known for d=2 and for d=3, the present example can be viewed as a demonstration by induction for the existence of such solitons in the case of arbitrary k.     

Pion-transfer (n, d) and (d, He) reactions leading to deeply bound pionic atoms

Theoretical studies are given on the (n, d) and (d, ³He) reactions leading to deeply bound pionic atoms in heavy nuclei of configuration [(nl)_π·j_n⁻¹]J. The cross sections for various pionic and neutron-hole configurations in the case of a ²⁰⁸Pb target are calculated at incident energies 300–1000 MeV/u by using the effective number approach and the eikonal approximation for distortion. The effective number with a pion in the 1s or 2p state and a neutron hole in the orbit peaks around the same incident energy (T_n = 600 MeV) as the elementary cross section n+n→d+π⁻, where the momentum transfer matches the angular-momentum transfer of L = 5–7. The DWIA cross section for (n,d) producing a pion in the 1s or 2p orbit at T_n = 600 MeV is found to be around 42 or 75 μb/sr, respectively. At T_n = 350 MeV, where the momentum transfer is small, quasi-substitutional states of configurations and are preferentially populated with (n, d) cross sections of 95 and 190 μb/sr, respectively. The (d, ³He) cross sections are estimated to be an order of magnitude smaller than the (n, d) cross sections. Thus, the (n, d) and (d, ³He) reactions are found to be suited for the production of deeply bound pionic atoms.     

Studies on the Ne(p, d)Ne and Ne(d, p)Ne reactions

Angular distribution measurements have been performed on the ²¹Ne(p, d)²⁰Ne and ²¹Ne(d, p)²²Ne reactions at E_p = 20 MeV and E_d = 10.2 MeV, respectively. In the ²¹Ne(p, d) ²⁰Ne reaction, the prolific formation of the J^π = 2⁺, 1.63 MeV state was characterized by l_n = 2 pickup, and the distribution associated with the 4⁴, 4.25 MeV state was suggestive of a weak l_n = 2 pickup. All of the observed l_n = 1 pickup strength is associated with formation of the 2⁻, 4.97 MeV ²⁰Ne level. The ²¹Ne(d, p)²²Ne results indicate that l_n = 2 transfer is involved in the formation of the 1.28, 3.36, 5.52, 5.63 and 6.65 MeV ²²Ne states. The angular distribution observed for the 2⁺, 4.46 MeV state and also the unresolved 5.33, 5.36 MeV composite of states required both l_n = 0 and l_n = 2 components in the associated distorted-wave Born approximation fits. The spectroscopic factors extracted from the present results are compared with those predicted by the Nilsson model without mixing: Applications of the angular momentum projection rule to the ²¹Ne(d, p)²²Ne reaction are considered.     

On the (d,Li) reaction

General features of the (d, ⁶Li) reaction are discussed in connections with some residual forces. An enhancement of ground state transitions among superconducting nuclei is found. Some examples in the lp shell are also worked out and coherence is found between the T = 0 and T = 1 channels of the residual force.     

Experimentelle Untersuchungen der Reaktionenp (d,pp) n undd (d,dp) n mit 51,5 MeV Deuteronen

The external beam of 51.5 MeV deuterons from the Karlsruhe isochronous cyclotron was used to investigate the three particle reactionsp(d,pp)n andd(d, dp)n. A kinematically complete experiment was performed by detecting the two emitted protons respectively the proton and the deuteron in coincidence. The data for the reactionp (d, pp) n exhibit a pronounced final state interaction between the outgoing neutron and one proton. This final state interaction is mainly due to then— p singlet interaction and the extractedn— p scattering length is ¦a_s¦=(19±2.5) fm. In the investigation of the reactiond(d, dp)n the angles were chosen as to observe quasielastic deuteron-proton-scattering predominantly. The data was analysed in terms of the Chew Low Spectator model and we obtained by “on-energy-shell” extrapolation for thed?p cross section the value (7±2.5) [mb/sr]. This value has to be compared with the cross section for freed?p scattering which was independently measured and the value obtained for the corresponding angle is (16±1) [mb/sr].     

Untersuchung der Niveaustruktur von53Cr und52Cr mit (d,d′) und (d,t)-Reaktionen

Angular distributions of deuterons and tritons from the reactions^52,53Cr(d,d),^52,53Cr(d,d′),^53,54Cr(d, t)^52,53Cr have been measured at E_d=11.8 to 11.9 MeV. The elastic scattering data have been analyzed in terms of the optical model. The (d, d′) and (d, t) data have been compared with DWBA calculations. Deformation parameters and spectroscopic factors have been extracted. The results are qualitatively discussed in terms of different nuclear models.     

O(d,d)-invariance in Inhomogeneous String Cosmologies with Perfect Fluid

In the first part of the present paper, we showthat O(d,d)-invariance usually known in a homogeneouscosmological background written in terms of proper timecan be extended to backgrounds depending on one or several coordinates [which may be anyspace-like or time-like coordinate(s)]. In all cases,the presence of a perfect fluid is taken into accountand the equivalent duality transformation in Einstein frame is explicitly given. In the second part,we present several concrete applications to somefour-dimensional metrics, including inhomogeneous ones,which illustrate the different duality transformations discussed in the first part. Note that most ofthe dual solutions given here do not seem to be known inthe literature.     

Enhanced electron screening in d(d,p)t for deuterated metals

The electron screening effect in the d(d,p)t reaction has been studied for deuterated metals, insulators, and semiconductors, i.e. 58 samples in total. As compared to measurements performed with a gaseous D₂ target, a large effect has been observed in most metals, while a small (gaseous) effect is found, e.g., for the insulators, semiconductors, and lanthanides. The periodic table provides the ordering of the observed small and large effects in the samples. An explanation of the large effects in metals is possibly provided by the classical plasma screening of Debye applied to the quasi-free metallic electrons. The data also provide information on the solubility of hydrogen in the samples.Received: 25 July 2003, Revised: 15 September 2003, Published online: 23 December 2003PACS: 25.10. + s Nuclear reactions involving few-nucleon systems - 25.45.-z ²H-induced reactions - 95.30.-k Fundamental aspects of astrophysicsFor the LUNA Collaboration; supported in part by BMBF (06BO812 and 05CL1PC1/1), GSI (Bo-Rol), DFG (Ro429/31-1 and 436Ung113), OTKA (T034259, T042733, F043408), and Dynamitron-Tandem-Laboratorium Bochum.