Y-89 MACS case

The MACS for Y-89 is fully determined by the resolved resonance region (neutron energies up to 100 keV), for kT = 5 keV. At higher temperatures, the MACS fraction covers up to 90% at kT = 30 keV, and up to 40% for kT = 100 keV. Here below, these estimates are shown for the capture cross section taken from the evaluated nuclear data file JENDL-4.0.

The MACS derived from the resolved resonance region (data file from 17-JAN-2022), measured at n_TOF, are given here below.

# kT in keV, MACS-kT in mb
# n_TOF-res    : eperimental kernel data file (data/ntof_17-JAN-2022)
# thermal      : 1128 +/- 20 mb (Mughabghab, 2018)
# total        : n_TOF-res (E <   94 keV) + thermal(1/v) + j40-he (E >   94 keV)
# ----- uncertainties -----
# E <   94 keV           :  5% from kernel + BG + norm
# therm(1/v)             :  2% (from thermal)
# E >   94 keV           : 10% assumed
# kT   n_TOF-res unc[mb] therm(1/v)   j40-he       n_TOF+1/v   unc[%]   unc[mb]     Total[mb]   unc[%]  unc[mb]
    5     69.68     3.48       2.54     0.00           72.22     4.82     3.48          72.22     4.82     3.48
    8     47.46     2.37       2.01     0.00           49.47     4.80     2.37          49.47     4.80     2.37
   10     39.65     1.98       1.79     0.01           41.45     4.78     1.98          41.46     4.78     1.98
   15     28.72     1.44       1.46     0.14           30.19     4.76     1.44          30.33     4.74     1.44
   20     22.78     1.14       1.27     0.54           24.05     4.74     1.14          24.59     4.64     1.14
   23     20.26     1.01       1.18     0.90           21.44     4.73     1.01          22.34     4.55     1.02
   25     18.84     0.94       1.13     1.17           19.98     4.72     0.94          21.15     4.49     0.95
   30     15.95     0.80       1.04     1.93           16.99     4.70     0.80          18.92     4.34     0.82
   35     13.70     0.69       0.96     2.71           14.66     4.67     0.69          17.37     4.24     0.74
   40     11.91     0.60       0.90     3.45           12.80     4.65     0.60          16.25     4.23     0.69
   45     10.44     0.52       0.85     4.12           11.28     4.63     0.52          15.40     4.32     0.66
   50      9.22     0.46       0.80     4.71           10.02     4.60     0.46          14.73     4.47     0.66
   55      8.20     0.41       0.77     5.21            8.96     4.58     0.41          14.18     4.68     0.66
   60      7.34     0.37       0.73     5.65            8.07     4.55     0.37          13.72     4.91     0.67
   70      5.97     0.30       0.68     6.33            6.65     4.49     0.30          12.97     5.39     0.70
   80      4.95     0.25       0.63     6.81            5.58     4.44     0.25          12.39     5.85     0.72
   90      4.16     0.21       0.60     7.16            4.76     4.38     0.21          11.92     6.26     0.75
  100      3.55     0.18       0.57     7.40            4.12     4.32     0.18          11.52     6.61     0.76

MACS plot and hi-res table

A comparison with the KADONIS-1.0 database and with the values available in the ENDF/B-VIII.0 (j80) and JENDL-4.0 (j40) libraries is shown in the figure below. A table with a much finer temperature grid is available here.

MACS vs temperature

DRC contribution?

DRC contribution to the capture cross section has been evaluated. The ground (2-) and first excited state (3- at 0.202 MeV) of ⁹⁰Y have a strong | ⁸⁹Y(1/2-) > ⊗ | 2d_5/2 > configuration, with their spectroscopic strength of the order of 50% each (see ENDSF). The second (0- at 1.21 MeV) and third (1- at 1.37 MeV) excited states have, in turn, a | ⁸⁹Y(1/2-) > ⊗ | 3s_1/2 > configuration, also with approximately 50% spectroscopic strength each. The p-wave DRC component to the MACS turns out to be less than 1 mb, for the whole range of temperatures in consideration here. Therefore, no DRC component has been added to the MACS.

JENDL-4 vs JENDL-5 libraries

The MACS calculations have been extended to include the evaluated data from the JENDL-5 nuclear data library (6 July 2023). Thedata set of calculations with the JENDL-5 library is reported here below. To be noted, in JENDL-5, a new resonance in Y-89 at 19.7 eV was added [1].

JENDL-5

# kT in keV, MACS-kT in mb
# n_TOF-res    : eperimental kernel data file (data/ntof_17-JAN-2022)
# thermal      : 1128 +/- 20 mb (Mughabghab, 2018)
# total        : n_TOF-res (E <   94 keV) + thermal(1/v) + j50-he (E >   94 keV)
# ----- uncertainties -----
# E <   94 keV           :  5% from kernel + BG + norm
# therm(1/v)             :  2% (from thermal)
# E >   94 keV           : 10% assumed
# kT   n_TOF-res unc[mb] therm(1/v)   j50-he       n_TOF+1/v   unc[%]   unc[mb]     Total[mb]   unc[%]  unc[mb]
    5     69.68     3.48       2.54     0.00           72.22     4.82     3.48          72.22     4.82     3.48
    8     47.46     2.37       2.01     0.00           49.47     4.80     2.37          49.47     4.80     2.37
   10     39.65     1.98       1.79     0.01           41.45     4.78     1.98          41.46     4.78     1.98
   15     28.72     1.44       1.46     0.14           30.19     4.76     1.44          30.33     4.74     1.44
   20     22.78     1.14       1.27     0.54           24.05     4.74     1.14          24.59     4.64     1.14
   23     20.26     1.01       1.18     0.90           21.44     4.73     1.01          22.34     4.55     1.02
   25     18.84     0.94       1.13     1.17           19.98     4.72     0.94          21.15     4.49     0.95
   30     15.95     0.80       1.04     1.93           16.99     4.70     0.80          18.92     4.34     0.82
   35     13.70     0.69       0.96     2.71           14.66     4.67     0.69          17.37     4.24     0.74
   40     11.91     0.60       0.90     3.45           12.80     4.65     0.60          16.25     4.23     0.69
   45     10.44     0.52       0.85     4.12           11.28     4.63     0.52          15.40     4.32     0.66
   50      9.22     0.46       0.80     4.71           10.02     4.60     0.46          14.73     4.47     0.66
   55      8.20     0.41       0.77     5.21            8.96     4.58     0.41          14.18     4.68     0.66
   60      7.34     0.37       0.73     5.65            8.07     4.55     0.37          13.72     4.91     0.67
   70      5.97     0.30       0.68     6.33            6.65     4.49     0.30          12.97     5.39     0.70
   80      4.95     0.25       0.63     6.81            5.58     4.44     0.25          12.39     5.85     0.72
   90      4.16     0.21       0.60     7.16            4.76     4.38     0.21          11.92     6.26     0.75
  100      3.55     0.18       0.57     7.40            4.12     4.32     0.18          11.52     6.61     0.76

The evaluated total MACS turned out to be consistent when using one or the other library for the high-energy part of the neutron energy dependent cross section (above 94 keV).

All libs

# kT in keV, MACS-kT in mb
# n_TOF-res    : eperimental kernel data file (data/ntof_17-JAN-2022)
# thermal      : 1128 +/- 20 mb (Mughabghab, 2018)
# total        : n_TOF-res (E <   94 keV) + thermal(1/v) + j50-he (E >   94 keV)
# ----- uncertainties -----
# E <   94 keV           :  5% from kernel + BG + norm
# therm(1/v)             :  2% (from thermal)
# E >   94 keV           : 10% assumed
#   1       2           3          4           5         6             7            8            9           10          11          12            13          14          15            16          17           18          19          20
#  kT      T6         total      unc[%]   n_TOF-res     unc[%]     ther(1/v)       DRC        j40-all     j40-res      j40-he       b80-all     b80-res      b80-he       j33-all     j33-res      j33-he       j50-all     j50-res      j50-he
  5.0   58.02483    72.21905    4.82473    69.68167    3.48408      2.53737      0.00000     72.13700    72.93454     0.00000      71.67300    72.57480     0.00000      71.69400    72.57480     0.00000      72.13300    72.93594     0.00000
  8.0   92.83974    49.47019    4.79769    47.46322    2.37316      2.00597      0.00000     49.67900    50.22168     0.00100      50.71900    50.71112     0.00234      50.73100    50.71112     0.00234      49.67700    50.22223     0.00100
 10.0  116.04967    41.45553    4.78318    39.65276    1.98264      1.79419      0.00000     42.03500    42.48373     0.00857      43.81700    42.96329     0.01789      43.82700    42.96329     0.01789      42.03400    42.48408     0.00857
 15.0  174.07450    30.32759    4.73640    28.72266    1.43613      1.46495      0.00000     31.52400    31.72164     0.13998      34.06900    31.25758     0.22888      34.07700    31.25758     0.22888      31.52300    31.72180     0.13998
 20.0  232.09934    24.58695    4.63868    22.78036    1.13902      1.26869      0.00000     25.98800    25.72350     0.53790      28.49400    24.32588     0.74915      28.50100    24.32588     0.74915      25.98700    25.72359     0.53790
 23.0  266.91424    22.33947    4.55314    20.25934    1.01297      1.18306      0.00000     23.74900    23.09791     0.89707      26.11600    21.32396     1.16970      26.12200    21.32396     1.16970      23.74900    23.09798     0.89707
 25.0  290.12417    21.15127    4.48999    18.84422    0.94221      1.13475      0.00000     22.53900    21.59699     1.17230      24.80200    19.64369     1.47650      24.80700    19.64369     1.47650      22.53900    21.59704     1.17230
 30.0  348.14901    18.91664    4.33886    15.95087    0.79754      1.03588      0.00000     20.19600    18.46379     1.92990      22.20400    16.25519     2.28350      22.20900    16.25519     2.28350      20.19600    18.46383     1.92990
 35.0  406.17384    17.37361    4.24244    13.70438    0.68522      0.95904      0.00000     18.51100    15.97266     2.71020      20.30200    13.69507     3.08490      20.30600    13.69507     3.08490      18.51100    15.97268     2.71020
 40.0  464.19868    16.25278    4.23446    11.90538    0.59527      0.89710      0.00000     17.24400    13.94401     3.45030      18.86000    11.70260     3.83380      18.86400    11.70260     3.83380      17.24400    13.94403     3.45030
 45.0  522.22351    15.40126    4.31770    10.43607    0.52180      0.84579      0.00000     16.25400    12.26727     4.11940      17.73300    10.11723     4.50830      17.73600    10.11723     4.50830      16.25400    12.26728     4.11940
 50.0  580.24835    14.72845    4.47416     9.21886    0.46094      0.80239      0.00000     15.45500    10.86614     4.70720      16.82600     8.83352     5.10180      16.82900     8.83352     5.10180      15.45500    10.86615     4.70720
 55.0  638.27318    14.17873    4.67920     8.19908    0.40995      0.76505      0.00000     14.79400     9.68468     5.21460      16.07800     7.77890     5.61620      16.08100     7.77890     5.61620      14.79400     9.68469     5.21460
 60.0  696.29802    13.71701    4.91065     7.33654    0.36683      0.73248      0.00000     14.23400     8.68048     5.64800      15.44800     6.90176     6.05770      15.45100     6.90176     6.05770      14.23400     8.68049     5.64800
 70.0  812.34768    12.97405    5.39287     5.96871    0.29844      0.67814      0.00000     13.33000     7.07966     6.32720      14.43600     5.53859     6.75440      14.43900     5.53859     6.75440      13.32900     7.07967     6.32720
 80.0  928.39735    12.39200    5.84879     4.94565    0.24728      0.63434      0.00000     12.62400     5.87631     6.81200      13.65200     4.54118     7.25600      13.65400     4.54118     7.25600      12.62400     5.87632     6.81200
 90.0 1044.44702    11.91747    6.25527     4.16181    0.20809      0.59806      0.00000     12.05400     4.95118     7.15760      13.02100     3.78978     7.61610      13.02300     3.78978     7.61610      12.05400     4.95118     7.15760
100.0 1160.49669    11.52044    6.60965     3.54876    0.17744      0.56737      0.00000     11.58400     4.22586     7.40430      12.50100     3.20988     7.87490      12.50200     3.20988     7.87490      11.58400     4.22587     7.40430

Reference

T Katabuchi et al., EJP A 57, 4 (2021)