On dielectric and magnetic relaxation phenomena and vectorial internal degrees of freedom in thermodynamics

It has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was derived and it was shown that Debye's theory for dielectric after-effects in polar liquids is a special case of the developed theory. In this paper it is shown that if Z is some vectorial internal degree of freedom which influences the polarization a new internal degree of freedom bip^(int) may be defined which is a function of biZ, which may replace biZ as vectorial internal degree of freedom and which is a part of the total specific polarization. Furthermore, p^(int) may be introduced in such a way that the remaining part of the polarization, p^(el) (defined by $\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}\text{=}\text{p}\text{?}\text{p}{}^{\mathrm{<mtext>int</mtext><mtext>)</mtext>}}$, where p is the total polarization per unit of mass), has the property that it vanishes for all values of p^(int) if the medium is in a state where the electric field E and the mechanical elastic stresses vanish and the temperature of the medium equals some reference temperature. If the equations of state are linearized the latter result implies for an isotropic medium $\text{E}\text{=ρa}{}^{\mathrm{(0,0)}}{}_{\mathrm{(bdp)}}\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}$, where ρ is the mass density and a^(0,0)_(P) a constant. On the other hand p^(int) satifies a relaxation equation. It is seen that the use of p^(int) as an internal degree of freedom is of great advantage. This is connected with the fact that p^(int) is a measurable quantity in contradistinction to an arbitrary “hidden” vectorial internal degree of freedom. Analogous results may be obtained for magnetic after-effects.     

Spectroscopy of states in 33S by means of neutron-gamma angular correlation measurements

Levels of ³³S for E_x < 5 MeV have been studied with the ³⁰Si(α, nγ)³³S reaction at bombarding energies of E_α = 7.5 and 10.2 MeV. Neutron-gamma angular correlation experiments lead to three unambiguous spin and parity assignments: $\text{J}{}^{\mathrm{\pi }}\text{(3.83) =}\text{5}\text{2}{}^{\mathrm{+}}\text{, J}{}^{\mathrm{\pi }}\text{(4.048) =}\text{9}\text{2}{}^{\mathrm{+}}\text{and}\text{J}{}^{\mathrm{\pi }}\text{(4.09) =}\text{7}\text{2}{}^{\mathrm{+}}$. The measured branching and mixing ratios yield transition strengths for dipole and quadrupole transitions.     

Multi-step processes in the interpretation of the 28Si(d, 3He)27Al reaction

Results from a CCBA analysis of the ²⁸Si(d, ³He)²⁷Al reaction are reported. The transfers are assumed to occur between dominant components of (λμ) symmetry (0, 12) and (2, 10) in the initial and final nuclear eigenstates respectively. The results show that cross sections to four of the six levels observed below 3 MeV can be fairly well reproduced within a pure K_(J) band framework. However, consistent with electromagnetic results, all six levels can be fit if the K_(J) band purity of the analysis, SU(3) model. $\text{5}\text{2}{}^{\mathrm{+}}\text{(}\text{ground and}\text{2.73}\text{MeV}\text{)}$ states and $\text{9}\text{2}{}^{\mathrm{+}}\text{(3.00}\text{MeV}\text{)}$ state is abandoned.     

Electron exchange between Fe2+ and Fe3+ ions on octahedral sites in spinels studied by means of paramagnetic Mössbauer spectra and susceptibility measurements

Mössbauer spectra were obtained of the paramagnetic spinels $\text{Zn}{}^{\mathrm{2+}}\text{|}\text{Zn}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>2</mtext>}}\text{Ti}{}^{\mathrm{4+}}{}_{\mathrm{<mtext>(1+x)</mtext><mtext>2</mtext>}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>(1?</mtext><mtext>x)</mtext>}}\text{Fe}{}^{\mathrm{2+}}{}_{\mathrm{x}}\text{|}\text{O}{}_4$ and susceptibilities were measured. The strong difference between the paramagnetic Fe²⁺ and Fe³⁺ spectrum, due to the different quadrupole splitting, is used for the distinction between the two species. At 300 K a superposition of the Fe³⁺ and the Fe²⁺ spectra is found for most of the iron and, in addition, some continuous absorption. The latter is strongest for equal Fe³⁺ and Fe²⁺ concentration $\text{(x =}\text{1}\text{2}\text{)}$ while it disappears towards the end members (Fe³⁺ only or Fe²⁺ only) as well as with decreasing temperature (between 78 and 200 K). From this it is concluded that it arises from thermally activated electron exchange, the frequency of which passes a “critical” value of ～10⁸ sec^?1 for increasing temperature. Paramagnetic susceptibilities are found to obey a Curie-Weiss law down to low temperatures. From the dependence of the asymptotic Curie temperature on the composition the magnetic interaction parameters J₁₁ = ?1.4 K, J₂₂ = ?3.3 K and J₁₂ = + 1.6 K for the Fe³⁺Fe³⁺, Fe²⁺Fe²⁺ and Fe³⁺Fe²⁺ interactions are derived. The experimental results are discussed in terms of a hopping model with an activation energy q ～- 0.12eV and a non-equivalence of the octahedral sites expressed by a varying potential energy difference U₀ between neighbouring sites. The continuous absorption at 300 K for $\text{x =}\text{1}\text{2}$ is attributed to about 17% of the iron on sites with U₀ running from 0 to ??0.06 eV. The ferromagnetic Fe³⁺, Fe²⁺ interaction (J₁₂) is attributed to electron transfer from localized Fe²⁺ ions to Fe³⁺ neighbours via a transfer integral b of the order of 0.05 eV. The magnitudes of J₁₂ and b are tentatively explained.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

Backward-angle high-resolution inelastic electron scattering on 40, 42, 44, 48Ca and observation of a very strong magnetic dipole ground-state transition in 48Ca

The search for magnetic dipole transitions from the ground state-even Ca isotopes to high lying J^π=1⁺ states by means of low momentum transfer but high resolution inelastic electron scattering is described. The previously detected strongly excited J^π=1⁺ state E_X=10.319 MeV [B(M1)↑=1.12±0.27μ_K²] in ⁴⁰Ca has been confirmed, but - contrary to the expectations of the independent particle shell model - only a fairly weak M1 transition is observed in ${}^{42}\text{Ca [E}{}_{\mathrm{<mtext>X</mtext>}}\text{= 11.235}\text{MeV}\text{, B(}\text{M}\text{1)↑=0.59±0.05 μ}{}^2{}_{\mathrm{<mtext>K</mtext>}}\text{]}$ and none in ⁴⁴Ca between E_{X=8.2?12.2 MeV}. In ⁴⁸Ca, however, a very strong M1 transition [B(M1) ↑ = 4.0 ± 0.3 μ²_K] to a single state at E_X=10.227 MeV has been discovered.     

X-band ESR studies of forbidden transitions of europium ions in CaF2: Eu crystals

The characteristics of allowed and forbidden transitions of Eu²⁺ ions in CaF₂ single crystals have been investigated at room temperature. The Angular dependences of these transition intensities were theoretically calculated with the use of perturbation theory, and compared with the experimental values. The experimental results can be explained by taking into account crystal field effects $\text{(}\text{1}\text{60}\text{) b}{}_4\text{[O}{}^0{}_4\text{+ 5O}{}^4{}_4\text{]}$, and a hyper fine interaction A_iS · I_i in the spin Hamiltonian.     

Author index

High-spin states in ^167,168Hf and ^{170, 171}W have been excited by the reactions ${}^{159}\text{Tb}\text{(}{}^{14}\text{N}\text{, x}\text{n}\text{)}{}^{\mathrm{173\; ?\; x}}\text{Hf and}{}^{155}\text{Gd}\text{(}{}^{20}\text{Ne}\text{, x}\text{n}\text{)}{}^{\mathrm{175\; ?\; x}}\text{W}$. The yrast bands have been observed up to $\text{J}{}^{\mathrm{\pi }}\text{=}\text{49}\text{2}{}^{\mathrm{+}}$ in ¹⁶⁷Hf, J^π = 28⁺ in ¹⁶⁸Hf, $\text{J}{}^{\mathrm{\pi }}\text{=}\text{45}\text{2}{}^{\mathrm{+}}$ in ¹⁷¹W and J^π = 22⁺ in ¹⁷⁰W. Both even-even nuclei display a strong backbend around J^π = 14⁺, whereas ¹⁶⁷Hf shows an upbend at ω ～- 0.33 MeV and ¹⁷¹W exhibits a progressive gain in aligned angular momentum above ω ～- 0.26 MeV. At even higher rotational frequencies, bridges have been found in the central valleys of the γ-γ correlation matrices at ω ～- 0.42 and 0.52 MeV for the Hf isotopes and ω ～- 0.45 and 0.47 MeV for the W isotopes. Deduced moments of inertia for the Hf isotopes using the correlation data show a smooth increase up to about the rigid-sphere value at ω ～- 0.5 MeV. The data are satisfactorily accounted for by cranked shell-model calculations. In particular, a qualitative interpretation is given for the experimentally observed systematic difference in the strength of the interaction potential for the N = 95 and N = 97 isotopes of Hf and W.     

A study of the K = 3nA1 - A2 centrifugal splitting in the 3ν2 and 4ν2 states of PH3 using a difference-frequency laser system

A frequency tunable infrared source has been constructed by using the (Ar-laser) - (dyelaser) difference frequency method developed by Pine and applied to the observation of the overtone bands of PH₃ 3ν₂ ← 0 and 4ν₂ ← ν₂ in the 3.4 μm region and 4ν₂ ← 0 in the 1.6-μm region. A Stark modulation method was used to increase the sensitivity of detection. For transitions which were well modulated, the minimum detectable absorption coefficient was estimated to be ～3 × 10^?7 cm^?1 using a 3-m cell. Emphasis was placed on the observation of the A₁-A₂ splitting for K = 3n rotational levels. For the 3ν₂ state splittings were observed for K = 3, 6, and 9 because PH₃ is a very nearly spherical top in this state. The magnitude and the J dependence of the observed K = 3n splittings have been analyzed by using a normal symmetric rotor Hamiltonian and a centrifugal distortion term of the form $\text{τ}{}_{\mathrm{xxxz}}\text{[(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)J}{}_{\mathrm{z}}\text{+ J}{}_{\mathrm{z}}\text{(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)]}\text{4}$.     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

Rotational constants of the E O+g state of I2 determined by polarization spectroscopy

The resonant 2-photon E(O⁺_g) ← B(O⁺_g) ← X(O⁺_g) transition of I₂ vapor has been studied by polarization spectroscopy, leading to a rotational analysis of the ν = 0–15 vibrational levels of the E state. The principal constants determined are $\text{B}{}_{\mathrm{e}}\text{= 19.9738(42) × 10}{}^{-3}\text{, α}{}_{\mathrm{e}}\text{= 5.602(84) × 10}{}^{-5}\text{, γ}{}_{\mathrm{e}}\text{= 1.02(41) × 10}{}^{-7}\text{, D}{}^{\mathrm{e}}{}_{\mathrm{J}}\text{= 3.040(74) × 10}{}^{-9}\text{cm}{}^{-1}\text{, and r}{}_{\mathrm{e}}\text{= 3.6470(5)}\text{A}\text{?}$.     

Resonances in the reaction 56Fe(p, γ)57Co

Resonances in the reaction ⁵⁶Fe(p, γ)⁵⁷Co have been surveyed over the energy range 1.2 ? E_p ? 1.5 MeV wherein the analogues of the ground state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}\text{, 0.014}\text{MeV}$ state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$ and 0.136 MeV state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}\text{)}$ of ⁵⁷Fe are expected to occur. Gamma-ray angular distributions have been used to establish resonance and bound-state spins, and decay schemes have been determined. The analogue resonances appear to be severely fragmented, however the density of resonances of a given spin correlates quite well with (³He, d) results and with the expected analogue-state positions.     

On the dynamics of itinerant electron magnets in the paramagnetic state

It is shown how disordered local-moment states, in a metal such as Fe, may be stabilized by constraining magnetic fields. Effective interaction parameters between moments are defined in terms of spin density functional theory. On removing the constraints the moments initially precess but then decay rapidly, the latter process leading to an energy width of S(q, ω) at large q of order $\text{(k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{C}}\text{W)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where T_C is the Curie temperature and W is the width of the d-band. T he consequences for neutron scattering experiments are discussed and the rather different case of Ni is considered.     

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.     

The 7Li(d, n0)8Be reaction with polarized 800 keV deuterons

The analysing power of the ${}^7\text{Li}\text{(}\text{d}\text{, n}{}_0\text{)}{}^8\text{Be}$ reaction for vector and tensor polarization of an 800 keV deuteron beam, as well as the relative cross section for the unpolarized beam were measured at 7 to 9 angles between 0° and 160°, using a thick target. Analysis in terms of (l, s, J^π) matrix elements shows that two intermediate states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{+}}$ and $\text{J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}$ present, strongly interfering with each other. Assignments to known ⁹Be levels and to threshold resonances as suggested by Hackenbroich and Seligman are briefly discussed. The magnitude of the vector analysing power makes the reaction interesting as a monitor for the vector polarization of low-energy deuteron beams.     

g-factors of 2.7 h 93Tc, 4.9 h 94Tc and 20 h 95Tc

The hyperfine splitting frequencies gμ_NB_H.F./h of 2.7 h ⁹³Tc $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$, 4.9 h ⁹⁴Tc (J^π = 7⁺) and 20 h ⁹⁵Tc $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$ as dilute impurities in Fe have been measured with NMR on oriented nuclei as 336.36(5) MHz, 175.11(1) MHz and 315.97(2) MHz, respectively. From the resonance shifts with an external magnetic field B₀ the hyperfine field of Tc$\text{Fe}$ has been determined as -317(5) kG. Taking this into account the nuclear g-factors are deduced as $\text{g(}{}^{93}\text{Tc}\text{) = 1.392(22), g(}{}^{94}\text{Tc}\text{) = 0.725(11)}\text{and}\text{g(}{}^{95}\text{Tc}\text{) = 1.308(21)}$.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

Tabulation of hyperfine splittings in rotational F1 and F2 levels of the ground vibrational state of 12CH4 for J ≤ 20

To a good approximation, hyperfine splittings for F₁ and F₂ rotational levels of the ground vibrational state of ¹²CH₄ depend linearly on three hyperfine interaction parameters. Coefficients in these linear expressions have been computed in a relatively simple manner and tabulated for levels with 1 ≤ J ≤ 20. The hyperfine pattern for the $\text{J = 7 F}{}_2{}^{\mathrm{(2)}}$ level computed from these expressions using values for the three hyperfine interaction parameters reported recently by Yi, Ozier and Ramsey (1) agrees well with the pattern obtained from new HeNe laser measurements of Hall and Bordé (2) on the $\text{P(7) F}{}_2{}^{\mathrm{(2)}}$ line of the ν₃ band of methane.