Interpreting data from polarized proton beams

The reactions pp → pp and pp → Δ⁺⁺n with polarized beam and/or polarized target are currently under investigation at the Argonne ZGS. We discuss how to interpret various measured quantities in terms of amplitudes whose behavior is familiar (as functions of s, t). For pp total cross sections and elastic scattering, Argonne measurements will yield Im ?₂ (s,t = 0) and the rather complicated combination $\text{2|?}{}_5\text{|}{}^2\text{+}\text{Re}\text{(?}{}_1\text{?}{}_2{}^1\text{? ?}{}_3\text{?}{}_4{}^1\text{)}$, where ?_i (i = 1, … 5) are conventional s-channel helicity amplitudes. The forward direction (t = 0) is of special interest. We find that for both pp → pp and pp → Δ⁺⁺n, polarized beam — polarized target experiments plus the rather general (testable) assumption that amplitudes with the same s-channel helicity flip quantum numbers are proportional, are sufficient to fully determine all non-vanishing amplitudes at t = 0. Numerical estimates of some observables, based on calculations in a specific model, are also given.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

A determination of the spin of the hypernucleus 12ΛB: (II). A complete analysis

The probability distribution calculated for the decay sequence ${}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.) →}{}^{12}\text{C}{}^1\text{π}{}^{\mathrm{?}}\text{→ αααπ}{}^{\mathrm{?}}$ passing through the (J^P_N) = (2⁺, 1) intermediate state ¹²C¹ (16.11 MeV) is cast in a symmetrical form and used to calculate the likelihood for $\text{J = 1}\text{relative to}\text{J = 2}\text{for}{}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.}\text{)}$ on the basis of the 85 examples available for this decay process. This procedure has optimum sensitivity, is free from the uncertainties of the comparisons previously made using only projected angular distributions, and strongly indicates that J^P = 1^? holds for ¹²_ΛB(g.s.). An appendix points out that all the data for the decay sequence passing through the (J^P_N, T) = (1⁺, 0) level of ¹²C¹ is well fitted for J = 1 if the J = 1 → J_n = 1 transition amplitude a_s1 takes a value in the range a_s1/s = 0.08 to 0.09.     

Calculation of the γγ → ϱ0ϱ0 cross section at high energies

The processes with the cross sections not decreasing with energy become important at high energies. The simplest processes of this kind are γγ → V_i⁰V_j⁰ where V⁰ = ?⁰, ω, ?, ….. We calculate their cross sections in the high-energy small angle region s ? |t| ? μ². The cross section γγ → ?⁰?⁰ at high energies (s ? 10 GeV²) exceeds those of γγ → ππ, ?⁺?^? considerably. At $\text{s ? 10}{}^4\text{GeV}{}^2$ (this is the characteristic energy for the VLEPP and SLC colliders) and $\text{|t| ? 2}\text{GeV}{}^2$, the ratio $\text{(}\text{d}\text{σ/}\text{d}\text{t)(γγ → ?}{}^0\text{?}{}^0\text{)/(}\text{d}\text{σ/}\text{d}\text{t)(γγ → μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{) ? 70}$.     

Microwave spectrum of dimethylketene: Centrifugal distortion and Coriolis interaction

For the prolate asymmetric (κ = ?0.58) top molecule dimethylketene the centrifugal constants have been determined in terms of the Δ constants by means of ΔK_? ≠ 0 rotational transitions. Two earlier assigned torsional excited states (01, 10)₁ and (01, 10)₂ of symmetry B₂ and A₂ of C_2v could be confirmed. A third fundamental vibration v_r(b₁), probably the inplane skeletal rock, has been found and analyzed in the v_r = 1 and v_r = 2 states. The variation of the centrifugal constants and of the inertial defects with the state of excitation could be explained by Coriolis coupling between the v_r(b₁) = 1 vibrational and v_t(b₂) = 1 torsional excited states. The Coriolis constant $\text{ζ}{}_{\mathrm{rt}}{}^{\mathrm{a}}$ and the torsional frequency ω_t(b₂) have been estimated to be $\text{ζ}{}_{\mathrm{rt}}{}^{\mathrm{a}}\text{≈ 0.24}$ and ω_r(b₁) - ω_t(b₂) ≈ 5.8 cm^?1, respectively.     

Investigation of the metastable state of Na2[Fe(CN)5NO] · 2H2O by optical spectroscopy. II The electronic spectra of the ground and metastable states

The absorption spectra of Na₂[Fe(CN)₅NO] · 2H₂O were measured in the visible region in the range of 3400–7000 Å. In the metastable state, an additional absorption band in the long wavelength range is observed and the transition $\text{2}\text{b}{}_{\mathrm{<mtext>2</mtext>}}\text{(d}{}_{\mathrm{xy}}\text{)→}\text{7}\text{e(π}{}^1\text{?NO}\text{)}$ becomes weaker in the excited state indicating a population of the π¹(NO)-orbital. The laser excited emission spectrum shows a broad luminescence beginning at the excitation line $\text{λ =}\text{5145}\text{A}\text{?}\text{(}\text{19,436 cm}{}^{-1}\text{)}$ with a maximum at about 6250 Å (16,000 cm^-1). A strong sharp luminescence at about 7836 Å is registered and may be assigned to a transition 3b₁(d_x²?y²) or 5a₁(d_z²) to the antibonding π¹(NO)- orbital. Further the broad luminescence is superimposed by a series of sharp spikes. These sharp spikes can also be observed for several days, when the laser is switched off, and are depending on the crystal orientation.     

Deviation from scaling in the triple-regge region of pp→ pX and fP universality

By generalizing $\text{f}\text{P}$ universality to Regge-particle “scattering” we obtain $\text{s}\text{d}\text{σ}\text{d}\text{t}\text{d}\text{M}{}^2\text{= F(}\text{s}\text{M}{}^2\text{,t)}$$\text{[1 +}\text{M}{}^{\mathrm{?1}}\text{b}{}_{\mathrm{<mtext>f</mtext>}}\text{(0)}\text{b}{}_{\mathrm{<mtext>P</mtext>}}\text{(0)}\text{]}$ for pp → pX, where b_f(t) and b_P(t) are the f and P Regge residues for, say, pp → pp. This agrees with the recent NAL data.     

Peripheral pn production and decay angular distributions in the reaction π−p → (pn)p at 12 GeV/c incident momentum

The reaction $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}$, where p_s is a slow proton, was measured at 12 GeV/c incident momentum with the CERN-OMEGA spectrometer. Both antiproton and proton were identified uniquely by electronics information. We obtained 1844 events with four-momentum Transfer squared in the range 0.13 ? |t| ? 0.33 GeV² and with invariant masses $\text{M(}\text{p}\text{n}\text{)}$ up to 2.5 GeV. The corresponding cross section in this t range is determined to be σ = 4 ± 0.4 μb. Extrapolating the differential cross section over the whole t range assuming dσ/dt ≈ exp(5.3t) we estimate a cross section of σ = 9.3 ± 2.0 μb. Comparison with data on $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ (where n_s is a slow neutron) in the same t range shows that the $\text{(}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}\text{and}\text{(}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ cross sections have approximately the same magnitude.     

Radiative lifetimes in MoI using a novel atomic beam source

Radiative lifetimes of the 4d⁵ (a⁶S)5pz ⁷P^o levels and the 4d⁵ (a⁶S)5pz⁵P^o levels in MoI are reported as follows: $\text{τ(}\text{z}{}^7\text{P}{}_4{}^{\mathrm{<mtext>O</mtext>}}\text{) = 15.9}\text{ns}$, $\text{τ(}\text{z}{}^7\text{P}{}_3{}^{\mathrm{<mtext>O</mtext>}}\text{) = 17.0}\text{ns}$, $\text{τ(}\text{z}{}^7\text{P}{}_2{}^{\mathrm{<mtext>O</mtext>}}\text{) = 17.1}\text{ns}$, $\text{τ(}\text{z}{}^5\text{P}{}_3{}^{\mathrm{<mtext>O</mtext>}}\text{) = 22.3}\text{ns}$, $\text{τ(}\text{z}{}^5\text{P}{}_2{}^{\mathrm{<mtext>O</mtext>}}\text{) = 22.1}\text{ns}$, and $\text{τ(}\text{z}{}^5\text{P}{}_1{}^{\mathrm{<mtext>O</mtext>}}\text{) = 21.7}\text{ns}$ (±5%). The lifetimes are measured using time resolved laser induced fluorescence and a novel atomic beam source. This novel hollow cathode effusive beam source produces an intense beam of ground state Mo atoms and metastable Mo atoms. Our measurements on the z ⁷P^O levels are in agreement with earlier lifetime measurements. Our measurements on the z ⁵P^O levels are the first direct radiative lifetime measurements of these levels; the z ⁵P^O measurements are of particular interest because the a⁵S → z⁵P^O multiplet is used to determine the solar abundance of Mo.     

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.     

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.     

Rotationally resolved spectra of two van der Waals states of I + Cl

Three-step optical resonance is used to execute state-selected transitions from the ground state of ICl to two van der Waals states, $\text{b(}\text{Ω}\text{= 1)}$ and $\text{b′(}\text{Ω}\text{= 2)}$, both of which correlate with the second dissociation limit, $\text{I}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) +}\text{Cl}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$, of ICl. Since the B(0⁺) state also belongs to this limit, three out of five states converging to I + Cl¹ are now accounted for. Principal constants of these states are: b′(2): T_e = 18275.84, ω_e = 31.093, ω_ex_e = 1.672, ω_ey_e = 0.0070, B_e = 0.034834, α_e = .001587, and D_e = 164.09 cm^?1; b(1): T_e = 18273.30, ω_e = 26.75, ω_ex_e = 0.882, B_e = 0.03579, q = 0.00084, and D_e = 166.63 cm^?1. In both states the equilibrium distance is near 4.2 Å, slightly greater than the sum of van der Waals contact radii, $\text{r}{}_{\mathrm{<mtext>I</mtext>}}\text{+ r}{}_{\mathrm{<mtext>Cl</mtext>}}\text{= 3.95}\text{A}\text{?}$. The large value of q in the b(1) state indicates that, in the basis set $\text{|j}{}_{\mathrm{a}}\text{j}{}_{\mathrm{b}}\text{j}\text{Ω}\text{〉}$ (a = I, b = Cl, j = j_a + j_b) the b(1) and b′(2) states belong to j = 1 and j = 2 “complexes,” respectively.     

Elastoresistivity of TTF-TCNQ and related compounds

Elastoresistances of TCNQ high conducting salts have been measured at room temperature by an original strain gauge technique. The effects, on the longitudinal and transverse resistivities ?, of an elementary uniaxial strain ? applied along one of the three axes, a, b or c¹ respectively, have been estimated.For TTF-TCNQ, they are:

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{a}}\text{=? ln ?}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{a}}\text{= 16±3}$

;

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{b}}\text{= ? ln α}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{b}}\text{= 34±4}$

;

(5% risk).So, in an hydrostatic pressure experiment, the fraction of piezoresistivity attributable to transverse effects is 43± 10% of the total value χ^b (K^b_a and K^b_c effects accumulated).Low values have been found for the anisotropy (?^a/?^b) variations due to strains. So one may write:

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{a}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{a}}\text{≌K}{}^{\mathrm{a}}{}_{\mathrm{b}}$

;

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{b}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{b}}\text{≌ K}{}^{\mathrm{b}}{}_{\mathrm{b}}$

;

.The TTF-, HMTTF-, TSF-, HMTSF-TCNQ elastoresistance values are coherent with the previously measured hydrostatic pressure piezoresistivity values.All these experimental results are in good agreement with a model where the longitudinal but also the transverse elastoresistivities are essentially due to variations with strains of the longitudinal scattering time τ_ν defined by σ^b = ne²τ_ν/m¹.     

The vibrational transition moment for the ν2 bands of 14ND3 and 15ND3

Intensities were measured at high pressure (200 Torr) for blended K-multiplets in the P and R branches of the s0 → aν₂ and a0 → sν₂ bands of ¹⁴ND₃. Intensities of 55 individual lines at 10 Torr of ¹⁵ND₃ were also measured by deconvolution of the true line shape from the observed vibration-rotation spectrum and the instrumental line shape. From these results we estimate a transition moment of 0.179 ± 0.010 D for both ¹⁴ND₃ and ¹⁵ND₃. These lead to a derivative of the dipole moment, $\text{|}\text{?μ}\text{?Q}{}_2\text{| = 93}\text{cm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{sec}{}^{\mathrm{?1}}$.     

A natural theory of the K-M mixing angles, weak and strong CP

We present a natural model in which the quark mass matrices are of the symmetric Fritzsch form with the two physically relevant phases $\text{σ = τ = ±}\text{π}\text{2}$. The model is natural in the sense of 't Hooft and explains all of the known aspects of the weak interaction phenomenology of the K-M matrix (including the weak CP) in terms of the observed quark mass eigenvalues only. The model solves the strong CP problem by the Peccei-Quinn mechanism while the phases $\text{σ = τ = ±}\text{π}\text{2}$ are generated by spontaneous symmetry breaking. The invisibility of the axion is more natural than in the existing models and is related to the absence of FCNC and the observed long b-quark lifetime. The key predictions of the model are m_t < 80 GeV and $\text{5.0 × 10}{}^{\mathrm{?3}}\text{? R}{}_{\mathrm{b}}\text{≡}\text{Γ(b→ue}\text{v}\text{)}\text{Γ(b→ce}\text{v}\text{)}\text{? 1.46 × 10}{}^{\mathrm{?2}}$, while the present experimental upper bound on R_b is 3 × 10^?2. The prediction on R_b is to be tested by experiments at CLEO and CUSB in the near future.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

The 2780 Å absorption system of thiophosgene

The vapor phase absorption spectrum of thiophosgene (Cl₂CS) in the 2500–2900 Å region consists of a broad intense band ($\text{log}\text{?}{}_{\mathrm{<mtext>max</mtext>}}\text{= 3.5}\text{at}\text{2540}\text{A}\text{?}$. On the red side of this a vibrationally discrete structure is found which becomes increasingly diffuse and merges into the broad band as the wavelength is decreased. It is shown that this vibrational structure can be explained as due to a $\text{π → π}{}^1$, ${}^1\text{A}{}_1\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ electronic transition between a planar ground state and a pyramidal excited state of the molecule. In the latter state, the CS stretching mode ν₁′(a₁) = 681 cm^?1 and the CCl bending mode ν₃′(a₁) = 147 cm^?1. From the inversion doublet splitting of the out-of-plane mode ν₄′(b₁), the barrier to inversion is calculated to be ～126 cm^?1, with an equilibrium out-of-plane angle of ～20°.     

First determination of the proton electromagnetic form factors at the threshold of the time-like region

From the measurement of $\text{B}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{=}\text{Γ(}\text{p}\text{p}\text{→}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}\text{Γ}\text{p}\text{p}\text{→total}\text{= (3.2 ± 10}{}^{\mathrm{?7}}\text{)}$, obtained in an experiment at CERN with antiprotons at rest, a value of the proton electromagnetic form factors at the threshold of the time-like region is derived: |G_E| = |G_M| = 0.51 ± 0.08 at q² = -3.52 (GeV/c)².     

Limits on the couplings of ϱ′ (1300 Me) and rhov;″ (1700 MeV) to the photon and to the (ππ) system

The analysis of the reaction e⁺e^?→π⁺π^? measured at the e⁺e^? colliding beam machine ADONE shows that, if ?′ and ?″ exist, the cross sections compare as follows (taking the ? as the reference point): $\text{σ(}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→ ? → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$: σ(e⁺e^? → ?′ → π⁺π^?): σ(e⁺e^? → ?″ → π⁺π^?) = 1: (7 ± 4) × 10^?3: (1 ± 5) × 10^?4. The square of the product of their couplings to the photon (γ_?) and the γγ system (g_?ππ) are derived.