Strong absorption and the distribution of zeros of the S-matrix

The only distributions normally included in a discussion of the statistical theory of nuclear resonance reactions are the distributions of the widths (Γ) and spacings (D) of the levels of the compound nucleus. However, as the usual Hauser-Feshbach theory makes clear, $\text{Γ}$ and $\text{D}$ alone are not sufficient to determine the ratio $\text{σ}{}_{\mathrm{cc\prime }}{}^{\mathrm{<mtext>dir</mtext>}}\text{σ}{}_{\mathrm{cc\prime }}{}^{\mathrm{<mtext>fl</mtext>}}$. In an attempt to determine what further statistical information is sufficient to determine this ratio, in the special limit that it tends to zero for all cc′, c ≠ c′ (the “strong-absorption” limit), we study several “picket fence” S-matrix models, as well as a random-residue model exhibiting Ericson fluctuations. These models indicate that the strong-absorption limit $\text{(}\text{S}{}_{\mathrm{cc\prime }}\text{= 0,}\text{all}\text{cc′)}$ is directly related to the distribution of the zeros of S_cc′(E) in the upper half of the complex E-plane, and that strong absorption is reached only if these zeros are distributed with a high density in the region E → + i ∞. As a by-product, we obtain a generalization of the theorem of Moldauer and Simonius $\text{[|}\text{det}\text{S}\text{| =}\text{exp}\text{(?π}\text{Γ}\text{/}\text{D}\text{)]}$. Our generalization applies to individual optical S-matrix elements (and so to direct-reaction cross sections) rather than just to their determinant.     

High-resolution photoemission study of adatom bonding effects: Cl (√2 × √2) R 45° on Cu (100)

We have investigated photoemission from an ordered $\text{(}\text{2}\text{×}\text{2}\text{) R 45°}$ Cl-overlayer on Cu (100) at good angular (Δθ ? 1°) and energy (ΔE = 100 meV) resolution. We observe two prominent adsorbate- induced features at 1.95 eV (FWHM ≈ 100 meV) and 5.4 eV (0.65 eV) below E_F. By determination of their angular momentum character, their spatial orientation and their energy dispersion, they are identified as “antibonding” and “bonding” resonances, respectively. Significant modification of the Cu d-band emission is observed and interpreted in terms of substrate orbitals which are involved in bonding.     

Phonon heating by hot electrons in n-InSb in quantizing magnetic fields

The effect of the phonon “narrow throat” was experimentally found in n-InSb in crossed electrical and quantizing magnetic fields at temperatures 1.6—4.2°K. The phenomenon of energy relaxation by hot electrons on phonons was detected with $\text{T}\text{S}\text{?}\text{h}\text{?}\text{λ}{}^{\mathrm{?1}}$ in the case of absence of a phonon thermal tank (S is sound velocity, λ is magnetic length, T is temperature). The value of a critical electric field (E_cr) on the S-type current-voltage characteristic (CVC) was measured as a function of temperature and the magnetic field.     

Diffusion and ionic conductivity in sodium beta alumina

Measurements of sodium tracer diffusion (D_t) and ionic conductivity (σ) have been made on the same single crystals of sodium beta-alumina of composition 1.23 Na₂0.11 Al₂O₃. The σ- measurements were made over the temperature 390–660 K using reversible (liquid sodium) electrodes. A fit to the conductivity data gives $\text{σT = 2470}\text{exp}\text{(?0.142}\text{eV}\text{kT}\text{)Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}\text{K}$. The D_t, measurements employed two techniques, i.e. nondestructive profiling over the temperature range 210–750 K and cation exchange over the temperature range 505–970 K. The results of the two techniques were in close agreement and can be expressed as $\text{D = 2.12 ×10}{}^{\mathrm{?4}}\text{exp}\text{(?0.169}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}{}^{\mathrm{?1}}$ for T>520K and $\text{D = 2.45 × 10}{}^{\mathrm{?4}}\text{exp}\text{(?0.164}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}\text{470}\text{K}$. The “transition” region between 470 and 520 K is not observed in the conductivity measurements. Silver cation exchange was used to determine the number of mobile sodium ions. A comparison of D_t and σ data yielded a Haven ratio that is temperature dependent, ranging in value from 0.45 at 870 K to 0.35 at 370 K.     

New inversion techniques for the triton photoeffect

The photoeffect cross section for a particle in a model potential has been calculated analytically along with five energy-weighted moments. Two sets of orthonormalized polynomials R_n and S_n are developed with the weighting functions $\text{exp}\text{(?x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ and $\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{exp}\text{(?x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. respectively. These polynomials are used to invert the calculated moments to get the cross section corresponding to 5, 4, 3 and 2 moments.The cross sections found by S-inversion are in good agreement with the model; those using R-inversion give somewhat poorer agreement.Clare and Lally calculated triton moments and used Laguerre inversion to find the triton cross section. We use their moments with R-inversion and S-inversion. Our resulting cross section agrees reasonably well with Gorbunov's and Faul's measurements of the ³He photoeffect. We find better agreement than that found by Clare and Lally.     

A numerical estimate of deviations from the exponential decay law for the transition 2P12→1S12 in hydrogen

The deviations from the exponential decay law of the $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states of the Dirac hydrogen atom with respect to the transition $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ are numerically estimated. We find |a₀(t) ? exp(?λt)|?2.5 × 10^?4 for all t, where a₀(t) is the “exact” decay amplitude and λ is a complex constant such that (2Re λ)^?1 is the “natural lifetime” of the $\text{2}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states with respect to the spontaneous transition to $\text{1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

Near 90° scattering in the channels K̄°p → π+Λ°, K̄°p → π+Σ° and KL°p → KS°p from 1.0 to 7.5 GeV/c

Differential cross sections for center of mass scattering angles near 90° are presented for the reactions $\text{K}\text{?}\text{°}\text{p}\text{→ π}{}^{\mathrm{+}}\text{Λ°}$, $\text{K}\text{?}\text{°}\text{p}\text{→ π}{}^{\mathrm{+}}\text{Σ°}$ and K_L°p → K_S°p in the momentum interval 1.0 to 7.5 GeV/c. The energy dependences of these cross sections are found to be equally well described by the parameterization: $\text{(}\text{d}\text{σ}\text{d}\text{Ω}\text{)}{}_{\mathrm{90°}}\text{∞ s}{}^{\mathrm{?2}}$ or $\text{(}\text{d}\text{σ}\text{d}\text{Ω}\text{)}{}_{\mathrm{90°}}\text{∞}\text{exp}\text{(? bp}{}_{\mathrm{\perp }}\text{)}$.     

Temperature shift of the CdxHg1−xTe energy gap

The temperature coefficient of the Cd_xHg_1?xTe energy gap dE_g/dT as a sum of lattice dilatation and the phonon-electron interaction terms has been calculated as the function of molar composition x, for 0?x?0.3, in the temperature range 4.2–300 K. A non-linear dependence of $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ vs x and a strong effect of temperature on $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ values have been obtained and a comparison with experimental data is discussed.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

Evidence for assignment of 14.0 MeV state in 11B from 10B(n,n)10B

The differential cross section and polarization for neutrons scattered from ¹⁰B have been measured at E_n = 2.63 MeV (E_x = 13.85 MeV). The results of this experiment and other available neutron scattering data in the range 1 < E_n < 4 MeV are interpreted through a single-level R-matrix calculation over the region 12 < E_x < 15 MeV. Based on this analysis the most probable J^π assignment for the 14.0 MeV level in ¹¹B is $\text{11}\text{2}{}^{\mathrm{+}}$. The anomaly near E_x = 13.1 MeV can only be explained in terms of two overlapping levels having assignments of ($\text{5}\text{2}$, $\text{7}\text{2}$)^? and ($\text{3}\text{2}$, $\text{5}\text{2}$, $\text{7}\text{2}$)⁺.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Failure of length scaling in Wilson's ϵ expansion

We show that length scaling of the four-point scattering amplitude in Wilson's ? expansion is not consistent in the order of ?³. However, in conformity with conformal invariance at the critical point, momentum scaling in a given channel is consistent. This latter method permits us to calculate the dimension of the field φ² at the critical point without recourse to length scaling and one finds $\text{d}{}_{\mathrm{\phi }}\text{2 =}\text{d}\text{2}\text{?}\text{1}\text{ν}\text{to O}\text{(?}{}^2\text{)}$ as if length scaling were true. However, this does not imply Kadanoff's relation 2?α = νd which is predicted on length scaling. Indeed the above-mentioned inconsistency makes impossible the determination of α by these methods.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Relativistic correction to the deuteron magnetic moment and angular condition

The relativistic correction (RC) to the deuteron magnetic moment is calculated using the light-cone dynamics. The restrictions imposed by the angular condition on the electromagnetic current operator of the deuteron are discussed in detail. It is shown that the additive model for the current operator of interacting constituents is consistent with the angular condition only for the two first terms of the expansion of the “good” current component $\text{j}{}_{\mathrm{+}}\text{=}\text{1}\text{2}\text{(j}{}_0\text{+ j}{}_{\mathrm{<mtext>z</mtext>}}\text{)}$ in powers of the momentum transfer q. The RC to μ_d is expressed through the matrix element of the “good” component j₊ and is found to be equal to $\text{(0.6–0.8) × 10}{}^{\mathrm{?2}}\text{e}\text{h}\text{?}\text{/2m}{}_{\mathrm{<mtext>p</mtext>}}\text{c}$ for realistic NN potentials. Taking account of RC decreases essentially the discrepancy between the theoretical and experimental values of μ_d. Possible solutions of the angular condition for squared q-terms of the j₊ current component are also discussed.     

Exciton binding energy in GaAs quantum wells deduced from magneto-optical absorption measurement

Magneto-optical absorption spectra due to exciton states and Landau-levels were measured in GaAs/AlAs multi-quantum-wells. By extrapolating the photon energies of the absorption peaks to zero magnetic field, the lowest state (1S) heavy hole exciton binding energy, E^B_$\text{h}$(1S), was obtained as a function of well size L_z in the range $\text{58}\text{A}\text{?}\text{?}\text{L}{}_{\mathrm{z}}\text{?252}\text{A}\text{?}$. The L_z dependence of E^B_h showed the change of the exciton character from three-dimensional to two-dimensional with decreasing L_z. The diamagnetic shift observed for the heavy hole exciton peak was larger than that for the light hole exciton peak, showing the anisotropic nature of the Luttinger-Kohn Hamiltonian. The diamagnetic shift of the heavy hole exciton peak became smaller as L_z was decreased, suggesting the enhancement of the two-dimensional exciton character.     

The application of XPS to the determination of the kinetics of the co oxidation reaction over the Ir(111) surface

The coverages of adsorbed oxygen and CO on an Ir(111) surface have been determined using X-ray photoelectron spectroscopy (XPS) during the steady-state catalytic production of CO₂. Correlating the coverages of the reacting adsorbates with the rate of CO₂ production allows the kinetics of the CO oxidation reaction to be determined. The reaction is found to obey a Langmuir-Hinshelwood rate expression of the form , where R_CO2 is the rate of CO₂ production, k⁰ is the pre-exponential factor of the reaction rate coefficient, [CO] and [O] are the surface coverages of CO and oxygen, respectively, and E_a is the activation energy for the oxidation reaction. The activation energy for this catalytic oxidation reaction is found to be approximately 9 $\text{kcal}\text{mole}$.     

A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

Target asymmetry and effective neutron polarization with polarized deuteron targets

A careful discussion is given of the definitions of “target asymmetry” and “effective neutron polarization” in the reaction $\text{d}\text{(γ,π}{}^{\mathrm{?}}\text{)2}\text{p}$ with polarized deuterons. The connection between the analyzing powers, T_q^k of the reaction and the target asymmetry, T is established taking into account the method of preparation of the polarized target. It is further shown that the concept of effective neutron polarization P_eff is valid only in a very approximate way, even when the target deuteron is purely vector polarized.