Angular distribution of $\gamma$ rays from neutron-induced compound states of ${}^{140}\mathrm{La}$

The angular distribution of individual $\gamma$ rays, emitted from a neutron-induced compound-nuclear state via radiative capture reaction of ${}^{139}\mathrm{La}(n,\gamma )$ has been studied as a function of incident neutron energy in the epithermal region by using germanium detectors. An asymmetry $A_{\mathrm{LH}}$ was defined as $(N_{\mathrm{L}}-N_{\mathrm{H}})/(N_{\mathrm{L}}+N_{\mathrm{H}})$, where $N_{\mathrm{L}}$ and $N_{\mathrm{H}}$ are integrals of low- and high-energy region of a neutron resonance respectively, and we found that $A_{\mathrm{LH}}$ has the angular dependence of $(Acos{\theta }_{\gamma }+B)$, where ${\theta }_{\gamma }$ is the emitted angle of $\gamma$ rays, with $A=-0.3881\pm 0.0236$ and $B=-0.0747\pm 0.0105$ in 0.74 eV $p$-wave resonance. This angular distribution was analyzed within the framework of interference between $s$- and $p$-wave amplitudes in the entrance channel to the compound-nuclear state, and it is interpreted as the value of the partial $p$-wave neutron width corresponding to the total angular momentum of the incident neutron combined with the weak matrix element, in the context of the mechanism of enhanced parity-violating effects. Additionally, we use the result to quantify the possible enhancement of the breaking of time-reversal invariance in the vicinity of the $p$-wave resonance.

Figure 1

Schematic of the ANNRI installed at beamline 04 of MLF at J-PARC: (A) collimator, (B) T0-chopper, (C) neutron filter, (D) disk chopper, (E) collimator, (F) germanium detector assembly, (G) collimator, (H) boron resin, and (I) beam stopper (iron).

Figure 2

Configuration of germanium spectrometer assembly.

Figure 3

Schematics of the upper seven type-A detectors: (A) electrode, (B) germanium crystal, (C) aluminum case, (D) BGO crystal, (E) $\gamma$-ray shield (Pb collimator), (F) neutron shield 1 (LiH 22.3 mm thick), (G) neutron shield 2 (LiF 5 mm thick), (H) neutron shield 3 (LiH 17.3 mm thick), and (I) photomultiplier tube for BGO crystal.

Figure 4

Schematics of type-B detectors: (A) Pb collimator, (B) carbon board, and (C) LiH powder.

Figure 5

Block diagram of signal processing. A signal from the germanium detector is divided into two branches: one for the timing and triggering and the other for the pulse height. In the branch of timing and triggering, the signal is converted to a bipolar signal. Signals over a threshold are triggered and the time of zero crossing determines the timing of the signal. In the branch of the pulse height, the signal is converted to a trapezoidal signal and the height of the trapezoidal from a baseline determines the pulse height of the signal.

Figure 6

${\partial }^2{I}_{\gamma }/\partial t^{\mathrm{m}}\partial E_{\gamma }^{\mathrm{m}}$ two-dimensional histogram of $\gamma$ rays with the lanthanum target as a function of timing $t^{\mathrm{m}}$ and deposited $\gamma$-ray energy $E_{\gamma }^{\mathrm{m}}$. The corresponding neutron energy $E_n^{\mathrm{m}}$ is also shown.

Figure 7

$\gamma$-ray counts relatively corrected by the incident beam intensity as a function of $t^{\mathrm{m}}$ for $E_{\gamma }^{\mathrm{m}}\ge 2\mathrm{MeV}$, which is referred as $\partial I_{\gamma }/\partial t^{\mathrm{m}}$.

Figure 8

Pulse-height spectrum of $\gamma$ rays $\partial I_{\gamma }/\partial E_{\gamma }^{\mathrm{m}}$ from the $(n,\gamma )$ reaction with a lanthanum target as a function of $E_{\gamma }^{\mathrm{m}}$.

Figure 9

Fit result of $p$-wave resonance. The curve shows the best fit.

Figure 10

Transitions from ${}^{139}\mathrm{La}+n$ to ${}^{140}\mathrm{La}$. Dashed line shows separation energy of ${}^{139}\mathrm{La}+n$.

Figure 11

Expanded $\partial I_{\gamma }/\partial E_{\gamma }^{\mathrm{m}}$. The dotted line shows the background determined by the simulation.

Figure 12

Magnified two-dimensional histogram.

Figure 13

$\partial N/\partial t^{\mathrm{m}}$ in the vicinity of the $p$-wave resonance for each ${\overline{\theta }}_d$. The central figure shows degrees in the direction of neutron momentum of the type-A detectors and the type-B detectors. The hexagons and the circles in the center of the figure denote each crystal of the type-A detector and type-B detector, respectively.

Figure 14

Visualization of the definitions of $N_{\mathrm{L}}$ and $N_{\mathrm{H}}$.

Figure 15

Angular dependencies of $N_{\mathrm{L}}$ and $N_{\mathrm{H}}$. The white point and black point show $N_{\mathrm{L}}$ and $N_{\mathrm{H}}$, respectively.

Figure 16

Angular dependence of $A_{\mathrm{LH}}$. The solid line shows the best fit.

Figure 17

Comparison of expanded $\partial I_{\gamma }/\partial E_{\gamma }^{\mathrm{m}}$ gated in the vicinities of $s_1$-wave resonance ($E_n^{\mathrm{m}}=0.2-0.4$ eV, black line), the $p$-wave resonance ($E_n^{\mathrm{m}}=0.6-0.9$ eV, shaded area with diagonal line), and the $s_2$-wave resonance ($E_n^{\mathrm{m}}=70-75$ eV, solid shaded area).

Figure 18

Visualization of the value of ${\varphi }_2$ on the $xy$ plane. The solid line and shaded area show the central values of the ${\varphi }_2$ and $1\sigma$ area, respectively. ${\varphi }_2$ denotes an angle of a point on a unit circle.

Figure 19

Value of $\left|\kappa \left(J\right)\right|$ as a function of ${\varphi }_2$. The solid line and shaded area show the central values of ${\varphi }_2$ and the $1\sigma$ area from the central value, respectively.

Figure 20

Angular dependencies of $N_{\mathrm{L}}-N_{\mathrm{H}}$ and $N_{\mathrm{L}}+N_{\mathrm{H}}$. The solid line indicates the best fit.

Figure 21

$a_1$ (straight lines) and $a_3$ (curved lines) on the $xy$ plane for the cases of $J_1=J_2=4$, $J_3=3$. The solid line, shaded area, dashed line, and dotted line show the central values of ${\varphi }_2$, $1\sigma$ areas, $2\sigma$ contours, and $3\sigma$ contours, respectively.

Figure 22

$a_1$ (straight lines) and $a_3$ (curved lines) on the $xy$ plane in the case of $J_1=J_2=J_3=3$. The solid line, shaded area, dashed line, and dotted line show the central values of ${\varphi }_2$, $1\sigma$ areas, $2\sigma$ contours, and $3\sigma$ contours, respectively.

Figure 23

Schematic of definition of the photopeak in the pulse-height spectrum.

Figure 24

Comparison of the pulse-height spectrum for $\gamma$ rays from a radioactive source ${}^{137}\mathrm{Cs}$ (gray line) and the numerical simulation (black line) for a type-B detector (left) and a type-A detector (right). Because the simulation faithfully reproduces the experimental data, these almost overlap.

Figure 25

Comparison of pulse-height spectrum for prompt $\gamma$ rays emitted in ${}^{14}\mathrm{N}(n,\gamma )$ reaction (gray line) and the numerical simulation (black line) for a type-A detector (left) and a type-B detector (right). Because the simulation faithfully reproduces the experimental data, these almost overlap.