New measurements of the n2P12,32 energy levels of Cs(I)

The energies of the $\text{n}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(7 ≤ n ≤ 13)}$ and $\text{n}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(7 ≤ n ≤ 27)}$ levels of CsI have been redetermined photographically from high resolution absorption measurements of the principal series lines $\text{6}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? n}{}^2\text{P}{}_{\mathrm{<mtext>J</mtext>}}$X. The new data disagree significantly [ ≈0.13 cm^-1] with the values given in the NBS-Tables of Moore¹ which are taken from a paper by Kratz.² By means of an extended Ritz-formula, the ionization energy of CsI was found to be 31406.46±0.03 cm^-1, which is, within the limit of uncertainty, in agreement with the data of Kleiman,³ Eriksson et al.,⁴ Bockasten,⁵ and Eriksson and Wenåker.⁶     

Quantum tunneling nucleation for superparamagnetic spin cluster reversals

Usual theories for time-dependent effects in superparamagnetism (over-turning of large spin clusters) assume a flip rate ^∝ exp (-U/kT). Instead, following Lifshitz and Kagan, we calculate the flip rate due to quantum-mechanical zero-point motion. The resulting “zero temperature” flip rate is R₀ exp (-cn) for a cluster with n spins. R₀ and c depend on domain wall energy and mass; typically, $\text{R}{}_0\text{= 10}{}^{13}\text{n}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{sec}{}^{-1}$ and c = 1.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Two-quasiproton states in 168Er studied by the 169Tm(t, α)168Er reaction

The ${}^{169}\text{Tm}\text{(}\text{t}\text{, α)}{}^{168}\text{Er}$ reaction has been studied using 17 MeV polarized tritons from the Los Alamos National Laboratory tandem Van de Graaff accelerator. The α-spectra were analyzed with a Q3D magnetic spectrometer. The overall energy resolution was typically ~ 15 keV (FHWM) and angular distributions of cross sections and analyzing powers were obtained for levels up to ~ 2.7 MeV. The fact that spins and parities for all levels up to ? 2 MeV were previously known from an extensive series of (n, γ) studies made it possible to determine specific two-quasiproton structures for many bands from the present results. The K^π = 2⁺ γ-vibrational band was found to have a large $\text{3}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ admixture, consistent with the predicted microscopic composition of this phonon, but no $\text{5}\text{2}\text{[413]}{}_{\mathrm{<mtext>p</mtext>}}\text{?}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ component was observed. The K^π = 0₄⁺ band at 1833 keV has ～ 25% of the $\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}\text{?}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ two-quasiproton strength. This is in excellent agreement with the Soloviev model but is inconsistent with the interacting boson model, in which the K^π = 0₄⁺ band is composed almost completely of multiphonon configurations that should not be populated in a single-nucleon transfer reaction. The $\text{K}{}^{\mathrm{\pi }}\text{= 4}{}^{\mathrm{?}}\text{,}\text{7}\text{2}{}^{\mathrm{?}}\text{[523]}{}_{\mathrm{<mtext>p</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{<mtext>p</mtext>}}$ two-quasiproton and the $\text{K}{}^{\mathrm{\pi }}\text{= 4}{}^{\mathrm{?}}\text{,}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}{}_{\mathrm{<mtext>n</mtext>}}\text{+}\text{1}\text{2}{}^{\mathrm{?}}\text{[521]}{}_{\mathrm{<mtext>n</mtext>}}$ two-quasineutron states are mixed strongly with each other, but the two K^π = 3^? bands composed of antiparallel couplings of the same particles are not. A good qualitative explanation of this mixing pattern is provided in terms of the effective neutron-proton interaction.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Level structure in 117Sb investigated in the decay of the isomeric three-quasiparticle state

The level structure of ¹¹⁷Sb was investigated in the reactions ¹¹⁵In(α, 2nγ)^117mSb, ¹¹⁷Sn(d, 2nγ)^117mSb and ¹¹⁷Sn(p, nγ)^117mSb. In order to confirm level sequences and to assign spins and parities to levels populated in the decay of the isomeric three-particle state $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ = 340 μs), prompt and delayed γ-ray spectra, lifetimes, γ-γ coincidences, γ-ray angular distributions, conversion electrons and excitation functions were measured. The spin $\text{25}\text{2}$⁺ of the isomeric state can be explained by the three-particle configuration [$\text{π(}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{); v(}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}^2\text{10}{}^{\mathrm{+}}\text{]}\text{25}\text{2}{}^{\mathrm{+}}$. This is supported by the experimentally determined g-factor of g = O.115 ± 0.006. Other levels in ¹¹⁷Sb can be interpreted as particle states coupled to anharmonic vibrations of the core. The existence of an excited $\text{9}\text{2}{}^{\mathrm{+}}\text{[404]}$ quasirotational band is experimentally proved and is supported by calculations of the equilibrium deformation.     

The 3540-Å electronic transition of malonaldehyde,a tunneling hydrogen-bonded molecule

Revised and more complete vibrational assignments are made for the 3540-Å $\text{π}{}^1\text{← n}$ band system of malonaldehyde. The $\text{0}{}^{\mathrm{+}}\text{0}{}^{\mathrm{?}}$ tunneling splitting is found to be 19 ± 11 cm^?1 for the $\text{nπ}{}^1$ state and this represents a 7-cm^?1 decrease relative to the ground electronic state. The tunneling splitting and the Franck-Condon envelope of intensities in the 185-cm^?1 upper-state progression suggest that the ${}^1\text{B}{}_1\text{(nπ}{}^1\text{)}$ state is significantly less tightly hydrogen-bonded than the ground ¹A₁ state.     

Observation of isomeric states and band structures in 107Cd

The odd-mass nucleus ¹⁰⁷Cd was investigated in the reactions ${}^{105}\text{Pd}\text{(α, 2}\text{n}\text{)}{}^{107}\text{Cd}\text{,}{}^{107}\text{Ag}\text{(d, 2}\text{n}\text{)}{}^{107}\text{Cd and}{}^{107}\text{Ag}\text{(}\text{p, n}\text{)}{}^{107}\text{Cd}$. The constructed level scheme is based on results, obtained from singles γ-ray spectra and excitation functions, from the measurements of delayed γ-rays, of γ-γ coincidences, of internal conversion electrons and of γ-ray angular distributions. Two new isomers were observed. The first one, interpreted as the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ neutron state at 845.6 keV has a half-life of 67 ± 6 ns. This isomeric state is populated by a strong E2 cascade. Bands built on the other intrinsic states with spins and parities $\text{5}\text{2}{}^{\mathrm{+}}$ and $\text{7}\text{2}{}^{\mathrm{+}}$ are not strongly populated. For the second isomeric state at an excitation energy of 2679 keV a half-life of 55±4 ns was determined. This isomer is probably a three-quasiparticle state. Its configuration can be proposed as $\text{[π(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?2}}{}_{\mathrm{8+}}\text{ν(}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^1\text{]}{}_{\mathrm{<mtext>21</mtext><mtext>2</mtext>}}{}^{\mathrm{+}}$.     

On the mobility of very pure semiconductors at very low temperatures

The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n₃ = 10¹³cm^?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration n_s, and has a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$-dependence (T: temperature).

$\text{μ = 0.3597\&z.xl;h}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{k(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^1{}^{\mathrm{<mtext>?3</mtext><mtext>4</mtext>}}$

, where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the ${}_{\mathrm{n}}{}_{\mathrm{s}}$-dependence for very pure semiconductors.     

Level structure of 48Sc from the 48Ca(p,nγ) reaction

Levels of ⁴⁸Sc up to 3.33 MeV excitation were studied by the reaction ⁴⁸Ca(p,nγ)⁴⁸Sc employing a variety of experimental techniques. A level scheme of ⁴⁸Sc comprising 29 excited states and 54 transitions were determined from the measurements of γ-γ coincidences and γ-ray excitation functions. Within the framework of the statistical compound nucleus model spins and parities of the ⁴⁸Sc levels were assigned from the angular distributions and linear polarizations of the de-excitation γ-rays as well as the excitation functions of the residual levels. From the present experimental results and other available data we tentatively identified some of the levels of the ($\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^9$, $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)}$, ($\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^9\text{, 2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$), ($\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^7\text{, 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) and ($\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^7\text{, 1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$) configurations in addition to the well-known ($\text{π}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, v}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) multiplet.     

General correction theorems on decomposition formulae of exponential operators and extrapolation methods for quantum Monte Carlo simulations

It is proved that the trace of the generalized Trotter formula $\text{Z(n) ≡ Tr[II exp(}\text{A}{}_{\mathrm{j}}\text{n]}{}^{\mathrm{n}}$ is an even function of n, when all A_j are symmetric, namely A^t_j = A_j, togethern with some generalizations. This yields a new extrapolatio n method of the form $\text{Z(n) ? Z(∞) + a/(n}{}^2\text{+ b)}$ for large n in quanntum Monte Carlo simulations.     

The Hilbert-Schmidt method in the three-particle problem and determination of the vertex parts tdn and td1n

Vertex constants for virtual decays $\text{t→d+n}\text{and}\text{t→d}{}^1\text{+n}$ are calculated using the resonance expansion technique for the three-particle amplitude suggested recently in ref. [1]. In the model with a spin-dependent separable NN-potential values $\text{G}{}_{\mathrm{<mtext>tdn</mtext>}}{}^2\text{=1.92}\text{fm}\text{, G}{}_{\mathrm{<mtext>td1n</mtext>}}{}^2\text{=?0.38}\text{fm}$ are obtained.     

Impurity conduction and negative magnetoresistance in compensated n type indium phosphide,at low temperature

Electrical resistivity, mobility, magnetoresistance in compensated n type InP with a carrier density n = 7,2 10¹⁶/cm³ have been measured in the temperature range 1,7 K – 100 K, in magnetic fields up to 0,9 Tesla. Under a temperature T_C, which corresponds to the formation of an impurity band in which the electron conduction is metallic, the magnetoresistance becomes negative. Longitudinal and transverse magnetoresistances have similar behaviours. Longitudinal magnetoresistance which is treated here, has the behaviour of a system of paramagnetic spins for which the Curie point is determined. The variation of the negative magnetoresistance versus magnetic field and temperature is quite well approximated by a Langevin function L(u) with $\text{u}\text{=}\text{μ}{}^1\text{B}\text{kT}$; $\text{μ}{}^1\text{=}\text{n}\text{μ}{}_{\mathrm{<mtext>B</mtext>}}$ is the effective magnetic moment where μ_B is the Bohr magneton and n = 5. The value of the effective magnetic moment and the average separation of donors, allow the discussion of the negative magnetoresistance on the basis of the Toyozawa model. Other models are discussed and it seems that in the range of impurity concentrations concerned, the picture of localised moments is more consistant that a “mobility edge” model.     

s- and p-wave neutron spectroscopy: Part VII. Widths of Neutron Resonances

Neutron reduced widths Γ_n⁰ and Γ_n¹ are reported for about 200 resonances observed in neutron total cross sections of Ca^{40, 44}, Ti⁴⁸, Cr^{50, 52, 54}, Fe^{54, 56}, Ni^{58, 60}, Sr⁸⁸, Y⁸⁹, Sn¹²⁴, Te¹³⁰, Ba^{136, 138}, and Pb^{206, 207, 208}, in the energy region 1 to 200 ^kev. Average parameters $\text{Γ}{}_{\mathrm{n}}{}^0$, $\text{Γ}{}_{\mathrm{n}}{}^0\text{D}$, and $\text{Γ}{}_{\mathrm{n}}{}^{\mathrm{(1)}}\text{D}$ have been derived and the Wigner distribution for local spacings and the Porter-Thomas distribution for reduced widths are verified for the resonances in the even-even nuclei Ca⁴⁰, Fe⁵⁶, Ni⁵⁸, and Ni⁶⁰. A simple method of area analysis which is less tedious and time consuming than the method reported before in Part III is also described.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Light composite fermions in a dynamical subquark model of pregauge interactions

The masses of composite leptons and quarks are discussed in a “dynamical subquark model of pregauge interactions”. In this model, the leptons and quarks are made of a spinor and scalar subquark with equal mass, M, and the gauge bosons and Higgs scalar of the SU(3)_c×SU(2)_L×U(1)_Y model are made of a subquark-antisubquark pair. The SU(2)_L×U(1)_Y symmetry is spontaneously broken by the composite Higgs scalar and the (scalar) subquark mass parameter is in turn bounded as $\text{M > 5.4}\text{TeV}\text{(=2π(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{where}\text{G}{}_{\mathrm{<mtext>F</mtext>}}$ is the Fermi coupling constant). The spontaneously generated mass of a lepton or quark, m_i⁽ⁿ⁾ (i = 1, 2; n = 1 ～ N_g), is calculated to be: $\text{m}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{× (4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)α}{}_{\mathrm{<mtext>e.m.</mtext>}}\text{(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/3}\text{6}\text{(=0.35r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{(4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)}\text{GeV}\text{),}\text{where}\text{r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}$ are the parameters satisfying that 0 ? r_i⁽ⁿ⁾ ? 1 and Σ (r_i⁽ⁿ⁾)² = 1;N_g is the total number of generations of the leptons and quarks; α_e.m. is the fine structure constant. The appearance of light composite fermions is related to a specific mechanism of generating global chiral symmetries of the leptons and quarks. Global symmetries of scalar subquarks yield chiral symmetries of the leptons and quarks. Our model turns out to satisfy 't Hooft's anomaly conditions on massless composite fermions.