High-resolution proton scattering on 50Ti

Differential cross sections were measured for ⁵⁰Ti(p, p) at four angles for E_p = 1.83 to 2.97 MeV, with an overall energy resolution of about 350 eV. Spins, parities and total widths were extracted for 212 levels. An energy region near E_p = 1.37 MeV was also examined in order to study the analogue of the ground state of ⁵Ti. Coulomb energies and spectroscopic factors were determined for the analogues of the ground and first excited states of ⁵¹Ti. The latter analogue was highly fragmented. The s-wave spacing and width distributions were analyzed and the number of missing levels estimated. The $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton strength functions were determined.     

The reaction 55Mn(d, t)54Mn

Neutron pick-up cross sections and vector analyzing powers have been measured for the reaction ⁵⁵Mn($\text{d}$, t)⁵⁴Mn at 17 MeV. The mixture of $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ to $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ transfer to the low-lying l_n = 1 states has been found. Evidence of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole nature of several strong l_n = 3 states above 1 MeV has been obtained.     

Das Niveauschema von 47V aus dem γ-zerfall von Analogresonanzen

A high-accuracy investigation of the level scheme of ⁴⁷V has been performed using the ⁴⁶Ti(p, γ)⁴⁷V reaction. The γ-decay schemes of the strong (p, γ) resonances at E_p = 1546, 1549, 1565 and 1572 keV lead to 17 new energy levels in ⁴⁷V with excitation energies between 2.7 and 5.1 MeV. From the (p,γ) angular distributions mixing ratios of the primary γ-transitions and J^π values of the resonances and of many states populated in the γ-decay have been determined. The total width of the E_p = 1549, 1565 and 1572 keV resonances for γ-decay are found to be Γ_γ = 0.12, 0.15 and 0.03 eV, respectively. The Q-value of the ⁴⁶Ti(p,γ)⁴⁷V reaction is found to be 5168.6 keV. The two resonances at E_p = 1549 and 1565 keV, which have $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}$, are interpreted as fine structure components of the analogue state of the $\text{E}{}^1\text{= 2.545}\text{MeV}\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}$ level in ⁴⁷Ti while the ($\text{7}\text{2}$) resonance at E_p = 1546 keV might correspond to the $\text{E}{}^1\text{= 2.615}\text{MeV}\text{7}\text{2}{}^{\mathrm{?}}$ parent state in ⁴⁷Ti. The analogue-antianalogue M1 transition strength of the split $\text{3}\text{2}{}^{\mathrm{?}}$ analogue state is 0.01 single-particle units and fits well into our systematics of IAS → AIAS transitions in fp-shell nuclei.     

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.     

The microwave spectrum of the SF radical

The rotational spectrum of the SF radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state was observed by using a source-modulation microwave spectrometer with a 1-m-long discharge cell. The SF radical was generated directly in the cell by a dc discharge in an $\text{OCS}\text{CF}{}_4$ mixture. A previous measurement of the microwave spectrum in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state was also extended to higher-J transitions. The least-squares analysis of all the observed spectral lines gave the B₀ rotational constant and the D₀ centrifugal distortion constant to be 16 576.9140(46) and 0.02924(10) MHz, respectively, where the values in parentheses denote 2.5 times the standard deviations. The Λ-doubling constant p_v was found to be extremely small, 3.409(44) MHz, and it was presumed that contributions of ²Σ⁺ and ²Σ^? states to the Λ doubling cancel each other. All the four fluorine hyperfine coupling constants were also determined, from which the spin density on the F atom was calculated to be 0.13.     

Infrared diode laser spectroscopy of the CF radical

The fundamental bands of the CF radical in the $\text{X}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{X}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ electronic states were observed by using an infrared tunable diode laser as a source. Zeeman modulation could be used in detecting lines not only in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, but also in ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, because the CF radical deviates considerably from Hund's case (a). From the least-squares analysis of the observed spectra, the following molecular constants were obtained: B_e = 1.416 704 (37) cm^?1, α_e = 0.018 419 (50) cm^?1, $\text{r}{}_{\mathrm{e}}\text{= 1.271 977 (17)}\text{A}\text{?}$, D_e = 6.68 (15) × 10^?6cm^?1, p₀ = 0.008 580 (21) cm^?1, p₁ = 0.008 52 (11) cm^?1, and $\text{ν}{}_0\text{= 1286.1281 (5)}\text{cm}{}^{\mathrm{?1}}$, with three standard errors in parentheses.     

Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

Gamma-ray transition probabilities in 91Nb+

The lifetimes of 14 excited states in ⁹¹Nb and lower bounds for 5 additional states were measured with the Doppler-shift attenuation method, utilizing the ⁹¹Zr(p, nγ)⁹¹Nb reaction. By using calibrated F(τ) curves, the uncertainty of the stopping power was reduced to about 15 %. Multipole mixing ratios were determined for several transitions from the γ-ray angular distributions. The experimental data on γ-ray transition probabilities were compared with theoretical values. These were calculated using shell-model wave functions based on a ⁸⁸Sr core and active protons in the $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$orbitals. For the negative-parity states also excitations of protons from the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ orbitals were taken into account.     

Study of the 58Ni(τ, α)57Ni reaction at 25 MeV

The ⁵⁸Ni(τ, α)⁵⁷Ni reaction has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 50° with a split-pole spectrometer up to 13.5 MeV excitation energy. A local zero-range DWBA analysis has been carried out, allowing l-assignments for about eighty levels, most of them previously unknown. An isospin-dependent potential has been used in the calculation of the neutron form factor for both T_<and T_> states, and the C²S values deduced using this procedure are compared to those obtained with the usual separation energy method. Analog states of eleven ⁵⁷Co levels have been identified and the eventuality for isospin mixing in ⁵⁷Ni has been discussed. A sum rule analysis has been carried out and energy centroids of hole states have been determined. About 60% of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ strengths and the full $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole strengths are observed. It is shown that the two excess neutrons in the ⁵⁸Ni ground state mainly populate the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbitals, whereas the occupancy number of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ subshell is found to be smaller than 0.1%. Some non-pickup angular distributions have also been observed and a CRC analysis assuming two-step processes in the (τ, α) reaction and weak-coupling wave functions for final states has been attempted. Assignments of J^π values are proposed for four ⁵⁷Ni levels, based on this analysis.     

The particle-hole spectra of 16O and 16N as observed in pick-up reactions from 17O

The reactions ¹⁷O(d, t) ¹⁶O and ¹⁷O(d, τ)¹⁶N have been investigated at E_d = 52 MeV. Energy spectra of tritons and τ-particles have been measured simultaneously up to excitation energies of 22 MeV in ¹⁶O and 10 MeV in ¹⁶N, respectively. Spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From the comparison of the t- and τ-spectra analog (T = 1) states in ¹⁶O could be identified and the distribution of T = 0 and T = 1 spectroscopic strengths could be deduced. Nearly the total $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole strengths have been found and the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{and}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole multiplets could be located both for T = 0 and T = 1. The average residual interactions in both shell-model configurations turned out to be strikingly different.     

Structure of positive parity states in 29P and two-step processes in (p,t) reactions

From a study of (p,t) reactions on ³¹P and ³⁰Si it is suggested that in ²⁹P the states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{1}\text{2}{}_2{}^{\mathrm{+}}$, the pair $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}_1{}^{\mathrm{+}}$, and the pair $\text{7}\text{2}{}_3{}^{\mathrm{+}}$, $\text{9}\text{2}{}_1{}^{\mathrm{+}}$ are related by weak coupling of a s${}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton with the states 0₁⁺, 0₂⁺, 2₁⁺ and 4₁⁺ respectively of ²⁸Si. Completely atypical L = 2 angular distributions have been obtained for the $\text{3}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{5}\text{2}{}_2{}^{\mathrm{+}}$ states in ²⁹P and it is suggested that this is due to contribution by two-step processes.     

Experimental and shell-model studies of the reactions 91Zr(d,p)92Zr and 90Zr(t,p)92Zr

The results of high-resolution studies of the ⁹¹Zr(d, p) reaction at E_d = 12 MeV and the ⁹⁰Zr(t, p) reaction at E_t = 11.85 MeV are presented. Absolute cross sections have been measured for both reactions and (d, p) spectroscopic factors determined. A comparison of these results with earlier data has been made, and although many of the previous assignments have been confirmed, many new features concerning the structure of ⁹²Zr have been discovered. Shell-model calculations have been performed for ⁹¹Zr and ⁹²Zr using a neutron space which includes the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{1}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbits and a proton space comprising the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits. Realistic proton-neutron and neutron-neutron interactions based on the Sussex matrix elements were used in the calculations. Spectroscopic factors have been calculated for the ⁹⁰Zr(d, p) and ⁹¹Zr(d, p) reactions and cross sections calculated for the ⁹⁰Zr(t, p) reaction. In general, good agreement between the theoretical and the experimental results has been obtained.     

Spectroscopic information on 35S and 37S from the (d,p) reaction

The reactions ³⁴S(d,p)³⁵S and ³⁶S(d,p)³⁷S were studied at the incident deuteron energy of 12.3 MeV. Proton groups were analysed using a multi-angle magnetic spectrograph with the resolving power $\text{E}\text{ΔE}\text{≈ 1400}$. Precise Q-values corresponding to 13 states of ³⁵S up to the excitation energy of 7483 keV and 22 states of ³⁷S up to the excitation energy of 6406 keV are presented. The ground-state transition Q-value for the reaction ³⁶S(d,p)³⁷S was found to be 2079.12 ± 0.13 keV. Angular distributions of proton groups corresponding to 6 states in ³⁵S and to 11 states in ³⁷S were analysed using DWBA calculations. Transferred orbital angular momenta and spectroscopic factors were deduced. Summed spectroscopic strengths show that substantial parts of single-particle strengths for $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in both reactions are exhausted b observed transitions.     

Low-lying levels of 140Pr

The doubly odd nucleus ¹⁴⁰Pr has been investigated by means of the ¹⁴¹Pr(d, t)¹⁴⁰Pr and ¹⁴⁰Ce(p, nγ)¹⁴⁰Pr reactions. Twenty-eight levels, up to 1300 keV excitation, were observed in the pickup study. DWBA analysis was used to determine l-values and spectroscopic factors for all but a few which are very weakly populated. Gamma-ray angular distributions, measured at E_p = 4.78 MeV for the five strongest γ-rays, show appreciable nuclear alignment and demonstrate the feasibility of such experiments in this mass region. Taken together, the two studies have permitted the identification of the 12 levels expected from the low-lying ($\text{π2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{ν2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$), ($\text{π2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{ν3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$), ($\text{π1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{ν2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) and (π1g_{$\text{7}\text{2}$}ν3s_{$\text{1}\text{2}$}^?1) configurations. Tenta assignments for the strong odd-parity states are suggested on the basis of their spectroscopic factors.     

Spectroscopic study of the N = 27 nuclei by means of the (τ, α) reaction

The (τ, α) reaction on ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe target nuclei has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 40° with a split-pole spectrometer in a large range of excitation energy. A local zero-range DWBA analysis has been carried out, using an isospin-dependent potential for the calculation of the neutron form factor, in order to get a coherent set of spectroscopic factors for both T_> and T_< levels in different nuclei. Assignments of l-values have been done for a large number of levels, most of them previously unknown, and energy centroids of hole states have been determined. Spectroscopic factors in ³⁹Ca, ⁴⁷Ti, ^{49, 52, 53}Cr have also been obtained for strongly excited states. A sum rule analysis has been carried out for the N = 27 nuclei: the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ hole strengths are generally fully exhausted by the observed levels, whereas only a fraction of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength has been evidenced. The $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, 1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states have been observed in all nuclei; in ⁵³Fe, the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states appear to be split in several components. In addition, a CRC analysis has been carried out for some levels with angular distributions not accounted for by a direct pick-up process. These levels are tentatively identified with states resulting from the coupling of one $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ neutron hole with excited states of the target nucleus. In particular, the $\text{5}\text{2}{}^{\mathrm{?}}\text{and}\text{9}\text{2}{}^{\mathrm{?}}$ members of the $\text{[2}{}^{\mathrm{+}}\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{]}$ configuration have been identified in each final nucleus. Unambiguous J^π assignments are made; and the two-step (τ, α) reaction therefo e appears as a useful spectroscopic tool, especially for investigating high spin states.     

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.     

Evidence for two narrow pp resonances at 2020 MeV and 2200 MeV

From the study of the reaction $\text{π}{}^{\mathrm{?}}\text{p→p}{}_{\mathrm{F}}\text{p}\text{p}\text{π}{}^{\mathrm{?}}$ using a fast proton (p_F) trigger device in the CERN Omega spectrometer, we find evidence for two narrow $\text{p}\text{p}$ states produced mainly in association with a Δ° (1232) and a N° (1520). The statistical significance of each peak is greater than 6 standard deviations. Masses and natural widths of these resonances are respectively M = 2020 ± 3 MeV, Λ₁ = 24 ± 12 MeV and M₂ = 2204 ± 5 MeV, Λ₂ = 16_?16⁺²⁰ MeV. Our data are consistent with a small production of the narrow ～ 1935 MeV resonance already reported. Production cross sections for these new $\text{p}\text{p}$ resonances are given.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Quantitative evidence of weak isospin mixing in the low-lying isobaric analog resonances in 209Bi

The excitation functions of ${}^{208}\text{Pb}\text{(}\text{p}\text{,}\text{p}{}_0\text{)}{}^{208}\text{Pb}$ have been measured in the energy range E_p = 14.2 to 17.4 MeV in 50 keV steps at θ_lab = 120°, 140° and 160°. The isobaric analog resonances of the parent states in ²⁰⁹Pb up to E_x = 2.5 MeV and the optical-model background were fit simultaneously at all energies and angles. The spreading widths and the values of a parameter β², which measures the isospin purity of the IAR, were determined for the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{,}\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{,}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, and $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ resonances. An average value of the isospin purity of β² = 66% was found.     

The γ-decay of the g92 analogue state in 59Cu

An investigation of the γ-decay of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ analogue state in ⁵⁹Cu has been performed using the ⁵⁸Ni(p, γ)⁵⁹Cu reaction. The (p, γ) excitation function has been taken in the range E_p = 3450–3650 keV. The decay schemes of the (p, γ) resonances at E_p = 3483, 3532 and 3547 keV, measured with Ge(Li) detectors, lead to eight new levels in ⁵⁹Cu with excitation energies between 1.8 and 4.7 MeV and to spin assignments of several states. The spins of the first two resonances are found to be ($\text{1}\text{2}$, $\text{3}\text{2}$) and ($\text{5}\text{2}$). The spin of the E_p = 3547 keV resonan is, from angular distributions, uniquely determined to be $\text{J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}$ and this state is found to be the unfragmented analogue state of the $\text{E}{}^1\text{= 3.062}\text{MeV}$, $\text{J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}$ parent state in ⁵⁹Ni. The measured complete decay scheme of this resonance shows that its isovector M1 decay is in disagreement with all existing theoretical predictions.