A model for phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ)

The observed phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ) are discussed using a simple model for the interchain coupling of charge density waves. Estimates based on Coulomb energies show that for 38 K < T < 49 K the components $\text{q}{}_{\mathrm{x}}\text{=}\text{π}\text{a}\text{+ q′}{}_{\mathrm{x}}$ and q_z of the wave vector associated with the charge density wave satisfy $\text{q}{}_{\mathrm{z}}\text{c}\text{q′}{}_{\mathrm{x}}\text{a?0.1}$, with $\text{q′}{}_{\mathrm{x}}\text{a～(T}{}_2\text{? T)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and T₂ = 49 K. A possible mechanism for the first order transition at 38 K is proposed. The results are compared with neutron and X-ray scattering and with isotope shifts of the transition temperatures.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

Average polarization of 12B in 12C(μ, ν)12B(g.s.) reaction: Helicity of the π-decay muon and nature of the weak coupling

The helicity, h^?, of μ^? in π-decay has been determined as positive (h^??+0.90) from the average polarization, P_av≡〈J_B·s_μ〉, of ¹²B produced in the $\text{μ}{}^{\mathrm{?}}\text{+}{}^{12}\text{C}\text{→ν}{}_{\mathrm{\mu }}\text{+}{}^{12}\text{B}$ reaction. We obtain also dynamical information on μ-capture: (i) the weak magnetism form factor, μ=4.5±1.1, and (ii) the sum of the induced pseudoscalar (g_p) and the 2nd class induced tensor (g_T) couplings versus g_A, ($\text{g}{}_{\mathrm{<mtext>P</mtext>}}\text{+g}{}_{\mathrm{<mtext>T</mtext>}}\text{)}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{=7.1±2.7}$. The latter result, adopting the “canonical” value of $\text{g}{}_{\mathrm{<mtext>P</mtext>}}\text{g}{}_{\mathrm{<mtext>A</mtext>}}$, leads to $\text{g}{}_{\mathrm{<mtext>T</mtext>}}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{=+1±2.7}$ which is compatible with zero and in strong contradiction with the value ?—6 recently advocated by Kubodera, Delorme and Rho.     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.     

Complexified Pöschl–Teller II potential model

With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where q_c=q₀e^2iαε, real V₁>0, q₀>0 and $\text{0<λε<}\text{π}\text{2}$. It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as $\text{PxP}{}^{\mathrm{-1}}\text{=}\text{ln}\text{q}{}_0\text{λ}\text{−x}$. The discrete energy eigenvalues are shown to be real when $\text{V}{}_2\text{⩾−}\text{q}{}_0\text{λ}{}^2\text{4}$ while they are complex conjugate pairs if $\text{V}{}_2\text{<−}\text{q}{}_0\text{λ}{}^2\text{4}$.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

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.     

Deuteron optical model calculations including a Tp tensor interaction

Deuteron-nucleus optical model calculations which include two types of tensor spin-orbit interactions are compared. The interactions considered are of the forms $\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>R</mtext>}}\text{(r)T}{}_{\mathrm{r}}\text{and}\text{1}\text{2}\text{[V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)T}{}_{\mathrm{p}}\text{+ T}{}_{\mathrm{p}}\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)]}$ where the operators T_r and T_p are defined as $\text{T}{}_{\mathrm{r}}\text{ (}\text{s}\text{·}\text{r}\text{?}\text{)}{}^2\text{?}\text{2}\text{3}\text{and}\text{T}{}_{\mathrm{p}}\text{ (}\text{s}\text{·}\text{p}\text{)}{}^2\text{?}\text{2}\text{3}\text{p}{}^2$. Here, $\text{s}\text{,}\text{r}\text{and}\text{p}$ are the deuteron spin, position, and momentum operators, respectively. If a physically reasonable radial dependence V_TP(r) is used, the S-matrix elements (and hence all observables) calculated using a T_p tensor potential are found to be similar to those calculated using a suitably chosen T_r potential, provided that the incident deuteron energy is small compared to the real central potential. At higher deuteron energies, the differences between the effects of T_r and T_p potentials are more pronounced.     

Spectroscopy of 62Ni with the 61Ni(d, p) reaction

Differential cross sections, vector and tensor analysing powers have been measured for the ⁶¹Ni(d, p) reaction at a deuteron energy of 12.3 MeV. Most of the 30 transitions observed below 8.5 MeV excitation are dominated by a single j-value, which was determined from behaviour of the analysing power data. For a number of transitions it was possible to make unambiguous j-assignment relying on the established j-dependence of the T₂₂ tensor analysing power. The deduced spectroscopic factors indicate that the full strength of neutron transfer to the ($\text{2p, 1f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$) and $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ orbits was found and seven $\text{5}\text{2}{}^{\mathrm{+}}$ transitions were located above 5.3 MeV. The separated strengths of the $\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{1}\text{2}{}^{\mathrm{?}}\text{and}\text{5}\text{2}{}^{\mathrm{?}}$ transitions are compared with shell-model calculations for the low-lying states of ⁶²Ni.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

On the transverse spread of QCD jets

Recent QCD results on two-particle longitudinal spectra inside quark and gluon jets are extended to the case of a fixed relative transverse momentum q_T with Λ ≈ 0.5 GeV ? 2|q_T| ? √Q². Broad q_T distributions, especially for gluon jets, are obtained which smooth out automatically the perturbative result and whose integrated versions scale in η_Max ≡ $\text{log}\text{(}\text{2q}{}_{\mathrm{<mtext>T</mtext>}}{}^{\mathrm{<mtext>Max</mtext>}}\text{Λ}\text{)/}\text{log}\text{(}\text{Q}\text{Λ}\text{)}$.     

Anisotropy of X-ray critical scattering in 4,4-di-n-hexyl-biphenyl liquid crystal

We have carried out a high-resolution X-ray critical scattering experiment in the isotropic phase connected with the isotropic-smectic-B transition in 4,4-di-n-hexyl-biphenyl. The measurements yield the following parameter values: $\text{d = 23.92}\text{A}\text{?}$, $\text{q}{}_0\text{= 0.268}\text{A}\text{?}{}^{\mathrm{?1}}$ and the critical exponents γ = 1.51 ± 0.12, ν_∥ = 0.65 ± 0.06, ν_⊥ = 0.70 ± 0.08. At the temperature t = 10^?3 ($\text{t =}\text{T}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{?1}$) the correlation lengths are $\text{ξ}{}_{\mathrm{\parallel }}\text{= 390}\text{A}\text{?}$ and $\text{ξ}{}_{\mathrm{\perp }}\text{= 1080}\text{A}\text{?}$.     

Reflection of long waves by interfaces

We derive comparison identities for waves satisfying the equation d²Ψ/dz²+q²(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by $\text{r=(1?2q}{}_1\text{q}{}_2\text{l}{}^2\text{)}\text{(q}{}_1\text{?q}{}_2\text{)}\text{(q}{}_1\text{+q}{}_2\text{)}$, where l is a legnth determined by the deviation of the interface profile from a step, and q₁, q₂ are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is $\text{t=(1+}\text{1}\text{2}\text{(q}{}_1\text{?q}{}_2\text{)}{}^2\text{l}{}^2\text{)}\text{2q}{}_1\text{(q}{}_1\text{+q}{}_2\text{)}$.     

Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.