Proton 1h112 excitations in odd-mass N = 82 nuclei

The structure of negative-parity states in odd-mass N= 82 isotones (135 ≦ A ≦ 145) is investigated in the framework of a model which is based on coupling one $\text{1h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ proton to π = + 1 states of the appropriate doubly-even isotonic core. It is shown that an effective model-space truncation can be achieved if only core states in the vicinity of the yrast line are taken into account. These have been selected from the several hundreds or even thousands of states obtained from shell-model calculations, where the $\text{1g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{3s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ single- are assumed to be occupied. Spectroscopic data are calculated and predictions on the structure of low-lying π = ? 1 states are discussed and compared as far as possible to experimental findings. Thereby, the particle-core coupling approach is shown to be capable of describing essential properties of negative-parity levels in the N = 82 nuclei considered.     

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($\text{a ≧ 0}$).     

Temperature shift of the CdxHg1−xTe energy gap

The temperature coefficient of the Cd_xHg_1?xTe energy gap dE_g/dT as a sum of lattice dilatation and the phonon-electron interaction terms has been calculated as the function of molar composition x, for 0?x?0.3, in the temperature range 4.2–300 K. A non-linear dependence of $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ vs x and a strong effect of temperature on $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ values have been obtained and a comparison with experimental data is discussed.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Collective properties of A = 117−127 odd-A I nuclei

Systematic ΔJ = 2 bands have been observed on the $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ quasi-proton states in A = 117?127 odd-I nuclei. The ΔJ = 2 energy spacings decrease (relative to the Te cores) as A decreases for the $\text{h}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ band but not for the others. Also ΔJ = 1 bands on unsually low-lying $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton-hole states exist.     

Johnson noise and absolute temperature

Experimental evidence using Josephson junction devices has suggested that Johnson noise in copper fails to be proportional to absolute temperature below 10 millikelvin. A microscopic theory is presented which gives the Johnson noise temperature $\text{T}{}_{\mathrm{<mtext>J</mtext>}}\text{= ?}{}_0{}^1\text{XT}{}_0$ coth ($\text{XT}{}_0\text{T}$) dX where $\text{T}{}_0\text{=}\text{hν}{}_{\mathrm{<mtext>F</mtext>}}\text{2kN}$. For copper, the calculated T₀ = 3.84 mK agrees closely with the value extracted from experimental data, 3.89 mK. Within a few percent, $\text{T}{}_{\mathrm{<mtext>J</mtext>}}\text{? (}\text{T}{}_0\text{2}\text{)}$ coth ($\text{T}{}_0\text{2T}$), and this adequately fits the available experimental data. ν_F is the fermi velocity and N is the length of the resistor. The Johnson noise parameter “T₀” presumably can measure ν_F along different crystal orientations.     

Electromagnetic transitions in some odd-proton deformed nuclei

In-beam measurements of nanosecond lifetimes applying the method of delayed γ-γ coincidences were performed in the (p, n) reaction. Analysing the time spectra with the centroid shift method, the following half-lives of excited nuclear states in the subnanosecond region could be found: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(353.2}\text{keV in}{}^{161}\text{Ho}\text{) = 0.52±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(252.7}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(579.4}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(431.2}\text{keV in}{}^{163}\text{Ho}\text{) = 0.37±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(439.9}\text{keV in}{}^{163}\text{Ho}\text{) = 0.35±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(471.3}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(612.8}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.3}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.6}\text{keV in}{}^{171}\text{Lu}\text{) = 0.85±0.20}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(469.2}\text{keV in}{}^{171}\text{Lu}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(357.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.40±0.08}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(449.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.58±0.12}\text{ns}$. Following half-lives in ¹⁷³Lu have been remeasured: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(425.3}\text{keV}\text{) = 0.84±0.20}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(434.9}\text{keV}\text{) = 0.38±0.10}\text{ns}$. Absolute γ-ray transition probabilities are deduced and compared with Nilsson model predictions including pairing correlations. Coriolis mixing calculations are performed for K-allowed as well as for K-forbidden transitions.     

Study by brillouin scattering of the C33 constant of thiourea submitted to an electric field

The C₃₃ constant is discontinuous for the lock-in transition at T₁ = 169 K. The variation ΔT₁ of the temperature of transition is a linear function of the applied electric field E and we find $\text{d}\text{T}{}_1\text{d}\text{E}\text{=0.82 deg.cm kV}{}^{\mathrm{?1}}$.Above a mean field E = 10 kV cm^?1 the transition observed for a first heating spreads on several degrees because damages appear in the incommensurate phase and the electric field becomes inhomogeneous.The results obtained at low fields are in very good accordance with the value of $\text{d}\text{T}{}_1\text{d}\text{E}$ calculated from the Clapeyron formula.Taking into account of the incommensurability of the phase above T₁, it can be shown that

$\text{dT}{}_1\text{dE}\text{=}\text{C}\text{2πP}{}_{\mathrm{o}}\text{3}\text{3}\text{?}\text{2}$

The knowledge of the spontaneous polarisation P₀ gives for the Curie constant C = 2.1 × 10³ K in qualitative agreement with the value deduced from measurements of the dielectric constant in the ferroelectric direction.     

Depinning by thermal fluctuations of the charge density wave in Peierls Fröhlich state

It is shown that the thermal fluctuations depin the charge density wave of the Peierls Fröhlich state pinned by impurities at absolute zero temperature. The critical temperature, T_d, of this depinning is estimated as $\text{T}{}_{\mathrm{d}}\text{= 0.55√}\text{m}{}^1\text{mγ}{}_0$ where m¹ and γ₀ are the mass of the collective mode and the pinning frequency at T = 0.     

Two theorems on the level order in potential models

We study the potentials of the form U(r)=?r^?1+λV(r), $\text{(}\text{d}\text{d}\text{r}\text{)(}\text{r}{}^2\text{d}\text{V}\text{d}\text{r}\text{)?0}$, and show that the energy levels satisfy the inequalities $\text{E(N}{}_{\mathrm{c}}\text{, l)?E(N}{}_{\mathrm{c}}\text{, l+1)}$ to first order in λ, where N_c denotes the coulombic principal quantum number and l the angular momentum. Similarly for potentials $\text{U(r)=r}{}^2\text{+λV(r), (}\text{d}\text{d}\text{r}{}^2\text{)}{}^2\text{V(r)?0}$, we prove to first order in λ that $\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{)?}\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{+2)}$, where NH denotes the harmonic oscillator quantum number. In the latter case, we give also quantitative restrictions on the relative positions at the lth and (l+1)th states.     

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.     

Competition cusps in (α, γ) reactions

Absolute cross sections are presented for the reactions ³⁷Cl(α, γ)⁴¹K for 2.90 MeV ≦ E^lab_α ≦ 5.23 MeV, ${}^{62}\text{Ni}\text{(α, γ)}{}^{66}\text{Zn}\text{for}\text{5.07}\text{MeV}\text{≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{?2}}\text{lab}\text{≦ 8.64}\text{MeV}\text{,}{}^{62}\text{Ni}\text{(α,}\text{n}\text{)}{}^{65}\text{Zn}$ for energies near the (α, n₀) threshold at $\text{E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{= 6.90}\text{MeV up to}\text{8.76}\text{MeV}\text{,}{}^{64}\text{Ni}\text{(α, γ)}{}^{68}\text{Zn for}\text{4.50 ≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{≦ 7.45}\text{MeV}$, and for ⁶⁴Ni(α, n)⁶⁷N from E_α^lab = 5.30 MeV up to E_α = 7.45 MeV. Substantial competition cusps were observed in the excitation function for all three (α, γ) reactions. The data were found to be in reasonable agreement with the predictions of the current versions of global Hauser-Feshbach models used in nucleosynthesis calculations. Including width fluctuation corrections and realistic neutron strength functions generally improves the ability of the models to predict the depth of the (α, γ) competition cusps; the depths of the predicted (α,γ) cusps are insensitive to the degree of isospin mixing. Taken together with studies of competition effects in proton-induced reactions, the present data confirm the importance of width fluctuation and strength function effects, and indicate essentially complete isospin mixing between T^< and T^> states in the compound nucleus.     

The cooperative Jahn-Teller effect in uranium (4+) hydroxy-sulphate

The magnetic susceptibility measurements of orthorhombic U(OH)₂SO₄ within the temperature range 4.2–300 K have revealed a magnetic anomaly at T_D = 21 K associated with crystallographic transition induced by the cooperative Jahn-Teller effect. Above 21 K the magnetic susceptibility of the uranium (4+) ion corresponds to the electronic ground doublet ${}_{\mathrm{¡}}\text{M}{}_{\mathrm{J}}\text{= ± 2〉}$ confirming thus the antiprismatic symmetry (D_4d) of the crystal field at the uranium site. Below T_D the system of two singlets ($\text{1}\text{√2}$)|2〉 ± ($\text{1}\text{√2}$)|$\text{2}$〉 separated by δ(T) is the ground state of the uranium ion.     

Ni2+ emission in MgO,KMgF3, KZnF3 and MgF2

The emission of Ni²⁺ ions in MgO, KMgF₃, KZnF₃ and MgF₂ crystals has been investigated. The fine structure on the bands at about 20 000 cm^-1 and 13 000 cm^-1 has been studied in detail and from this and the excitation spectra these bands are assigned to ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{A}{}_{\mathrm{2g}}$ and ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{T}{}_{\mathrm{2g}}$ transitions respectively.     

Kerr-effect and dielectric tensor elements of magnetite (Fe3O4) between 0.5 and 4.3 eV

The complex polar Kerr effect (rotation and ellipticity) of magnetite single crystals has been measured at room temperature between 0.5 and 4.3 eV. From the magneto-optical data and the optical constants, the off-diagonal elements (?_xy) of the dielectric tensor has been derived. Three well separated magneto-optical transitions have been indentified. At about 0.75 eV one strong magneto-optical structure with a diamagnetic line shape is assigned to a $\text{3d}{}^6\text{→3d}{}^5\text{(}{}^6\text{A}{}_{\mathrm{1g}}\text{) 4s}$ transition from Fe²⁺ in octahedral sites. Two other structures with paramagnetic line shapes near 1.85 and 2.90 eV are assigned to the orbital promotion processes $\text{3d}{}^6\text{(Fe}{}^{\mathrm{2+}}{}_{\mathrm{oct}}\text{)→3d}{}^5\text{(}{}^4\text{T}{}_{\mathrm{1g}}\text{) 4s}$ and $\text{3d}{}^5\text{(Fe}{}^{\mathrm{3+}}{}_{\mathrm{tet}}\text{)→3d}{}^4\text{(}{}^5\text{T}{}_2\text{) 4s}$, respectively, which take into account Fe 3d^n?1 final state effects.     

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.     

Classification of the Yang-Mills anomalies in even and odd dimension

The general solution to the Wess-Zumino consistency equation is constructed. It does not depend on the antighost, nor on the sources, but only on the gauge and ghost fields through the geometrical combination $\text{A}\text{?}\text{= A}{}_{\mathrm{\mu }}\text{d}\text{x}{}^{\mathrm{\mu }}\text{+c}$. In dimension d, the anomalies with ghost number g are related to the off-BRS (d+s)-closed exterior forms $\text{I(}\text{A}\text{?}\text{, F)}$, of degree d + g + 1 and at most g-linear in $\text{A}\text{?}\text{.}$     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

Generalized neutron particle-hole states in an extended unified model

Negative-parity levels in the doubly even N = 82, Z nuclei, with 3.0 MeV ? E_x? 6.0 MeV are described in an extended unified-model approach, where neutron hole states in the Z = 50, N = 82 closed shell core, (i.e. ) are coupled to the low-lying levels (E_x ? 2.0 MeV) of the odd-neutron N = 83, Z nuclei. This particular configuration space of generalized neutron particle-hole states (GNPH) is particularly suited for describing negative-parity levels obtained in proton inelastic scattering through isobaric analogue resonances (IAR), corresponding to the N = 83, Z low-lying nuclear levels. Level schemes as well as partial decay widths and angular distributions are calculated and compared extensively with the available experimental data. Also spectroscopic factors, as well as wave functions, deduced from the experimental results are studied in detail. Thus in the cases of ¹³⁶Xe, ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd and ¹⁴⁴Sm, some of the important neutron particle-hole configurations can uniquely be determined in the energy region 3.0 MeV ?E_x ? 6.0 MeV.     

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.