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How to truncate
kshell_ui.py asks you if you want to truncate the model space. For large configurations (many valence nucleons and many shells for them to occupy) truncation might be necessary for KSHELL to actually complete the calculations. We use V50 with the GXPF interaction as an example. This configuration has a dimensionality of:
2*M M-scheme dim. J-scheme dim.
dim. 44 4 4 4.00x10^ 0 4.00x10^ 0
dim. 42 46 42 4.60x10^ 1 4.20x10^ 1
dim. 40 263 217 2.63x10^ 2 2.17x10^ 2
dim. 38 1069 806 1.07x10^ 3 8.06x10^ 2
dim. 36 3489 2420 3.49x10^ 3 2.42x10^ 3
dim. 34 9737 6248 9.74x10^ 3 6.25x10^ 3
dim. 32 23975 14238 2.40x10^ 4 1.42x10^ 4
dim. 30 53304 29329 5.33x10^ 4 2.93x10^ 4
dim. 28 108622 55318 1.09x10^ 5 5.53x10^ 4
dim. 26 205136 96514 2.05x10^ 5 9.65x10^ 4
dim. 24 362005 156869 3.62x10^ 5 1.57x10^ 5
dim. 22 600850 238845 6.01x10^ 5 2.39x10^ 5
dim. 20 942669 341819 9.43x10^ 5 3.42x10^ 5
dim. 18 1403670 461001 1.40x10^ 6 4.61x10^ 5
dim. 16 1990227 586557 1.99x10^ 6 5.87x10^ 5
dim. 14 2694122 703895 2.69x10^ 6 7.04x10^ 5
dim. 12 3489341 795219 3.49x10^ 6 7.95x10^ 5
dim. 10 4331494 842153 4.33x10^ 6 8.42x10^ 5
dim. 8 5160580 829086 5.16x10^ 6 8.29x10^ 5
dim. 6 5907365 746785 5.91x10^ 6 7.47x10^ 5
dim. 4 6502475 595110 6.50x10^ 6 5.95x10^ 5
dim. 2 6886407 383932 6.89x10^ 6 3.84x10^ 5
dim. 0 7019100 132693 7.02x10^ 6 1.33x10^ 5
which is too large to run on a regular computer for any decent amount of requested levels. Lets see how the dimensionality changes with truncation. When kshell_ui.py asks for truncation, enter 1 to apply particle-hole truncation:
truncation for "+" parity state in V50_gxpf1a_p.ptn
truncation scheme ?
0 : No truncation (default)
1 : particle-hole truncation for orbit(s)
2 : hw truncation
3 : Both (1) and (2)
1
which outputs:
# n, l, j, tz, spe
1 0 3 7 -1 -8.624 p_0f7/2
2 1 1 3 -1 -5.679 p_1p3/2
3 0 3 5 -1 -1.383 p_0f5/2
4 1 1 1 -1 -4.137 p_1p1/2
5 0 3 7 1 -8.624 n_0f7/2
6 1 1 3 1 -5.679 n_1p3/2
7 0 3 5 1 -1.383 n_0f5/2
8 1 1 1 1 -4.137 n_1p1/2
specify # of orbit(s) and min., max. occupation numbers for restriction
# of orbit(s) for restriction? (<CR> to quit):
Here we see the valence orbitals 0f7/2, 1p3/2, 0f5/2 and 1p1/2, for both protons and neutrons. The l column denotes the angular momentum of the orbital, j the total angular momentum of the orbital, and tz the isospin. Let us now restrict the number of protons and neutrons allowed in the 0f7/2 orbital. In the above table we can see that the 0f7/2 orbitals are labeled 1 (protons) and 5 (neutrons). Set the maximum number of protons and neutrons to 2 in those orbitals by:
# of orbit(s) for restriction? (<CR> to quit): 1,5
min., max. restricted occupation numbersfor the orbit(s) (or max only) : 2
We now check the dimensionality of the truncated configuration:
2*M M-scheme dim. J-scheme dim.
dim. 36 5 5 5.00x10^ 0 5.00x10^ 0
dim. 34 58 53 5.80x10^ 1 5.30x10^ 1
dim. 32 303 245 3.03x10^ 2 2.45x10^ 2
dim. 30 1148 845 1.15x10^ 3 8.45x10^ 2
dim. 28 3474 2326 3.47x10^ 3 2.33x10^ 3
dim. 26 8930 5456 8.93x10^ 3 5.46x10^ 3
dim. 24 20129 11199 2.01x10^ 4 1.12x10^ 4
dim. 22 40732 20603 4.07x10^ 4 2.06x10^ 4
dim. 20 75106 34374 7.51x10^ 4 3.44x10^ 4
dim. 18 127691 52585 1.28x10^ 5 5.26x10^ 4
dim. 16 201896 74205 2.02x10^ 5 7.42x10^ 4
dim. 14 298865 96969 2.99x10^ 5 9.70x10^ 4
dim. 12 416333 117468 4.16x10^ 5 1.17x10^ 5
dim. 10 547983 131650 5.48x10^ 5 1.32x10^ 5
dim. 8 683573 135590 6.84x10^ 5 1.36x10^ 5
dim. 6 810023 126450 8.10x10^ 5 1.26x10^ 5
dim. 4 913390 103367 9.13x10^ 5 1.03x10^ 5
dim. 2 981186 67796 9.81x10^ 5 6.78x10^ 4
dim. 0 1004814 23628 1.00x10^ 6 2.36x10^ 4
where we see that the dimensionality has been reduced by up to an order of magnitude for some angular momenta.
Some model spaces, like the model space of sdpf-mu, span several major shells. In this case we can use hw (hbar omega) truncation to limit the number of particles which are allowed to cross the major shell gap. Lets use sdpf-mu interaction has a dimensionality so large that we are not even able to calculate the dimensionality, let alone perform the calculations. Here we need to use hw truncation to drastically reduce the size. Choose option 2 when you are prompted for truncation (or option 3 if you plan on using particle-hole truncation in addition to hw), and lets apply a truncation which allows a maximum of 3 particles to be excited across the major shell gap at the same time:
truncation for "+" parity state in Sc44_sdpf-mu_p.ptn
truncation scheme ?
0 : No truncation (default)
1 : particle-hole truncation for orbit(s)
2 : hw truncation
3 : Both (1) and (2)
2
(min. and) max hw for excitation : 3
lowest hw, maxhw 60 63
generating partition file ............ done.
In the case of sdpf-mu you will be prompted for truncation of the negative parity levels too. This example uses the same truncation for both
2*M M-scheme dim. J-scheme dim.
dim. 42 8 8 8.00x10^ 0 8.00x10^ 0
dim. 40 84 76 8.40x10^ 1 7.60x10^ 1
dim. 38 513 429 5.13x10^ 2 4.29x10^ 2
dim. 36 2250 1737 2.25x10^ 3 1.74x10^ 3
dim. 34 7950 5700 7.95x10^ 3 5.70x10^ 3
dim. 32 23800 15850 2.38x10^ 4 1.58x10^ 4
dim. 30 62464 38664 6.25x10^ 4 3.87x10^ 4
dim. 28 146820 84356 1.47x10^ 5 8.44x10^ 4
dim. 26 313940 167120 3.14x10^ 5 1.67x10^ 5
dim. 24 617562 303622 6.18x10^ 5 3.04x10^ 5
dim. 22 1127352 509790 1.13x10^ 6 5.10x10^ 5
dim. 20 1922531 795179 1.92x10^ 6 7.95x10^ 5
dim. 18 3079113 1156582 3.08x10^ 6 1.16x10^ 6
dim. 16 4651003 1571890 4.65x10^ 6 1.57x10^ 6
dim. 14 6648334 1997331 6.65x10^ 6 2.00x10^ 6
dim. 12 9018026 2369692 9.02x10^ 6 2.37x10^ 6
dim. 10 11633108 2615082 1.16x10^ 7 2.62x10^ 6
dim. 8 14296260 2663152 1.43x10^ 7 2.66x10^ 6
dim. 6 16760154 2463894 1.68x10^ 7 2.46x10^ 6
dim. 4 18762983 2002829 1.88x10^ 7 2.00x10^ 6
dim. 2 20072284 1309301 2.01x10^ 7 1.31x10^ 6
dim. 0 20527802 455518 2.05x10^ 7 4.56x10^ 5
and
2*M M-scheme dim. J-scheme dim.
dim. 50 6 6 6.00x10^ 0 6.00x10^ 0
dim. 48 95 89 9.50x10^ 1 8.90x10^ 1
dim. 46 735 640 7.35x10^ 2 6.40x10^ 2
dim. 44 3972 3237 3.97x10^ 3 3.24x10^ 3
dim. 42 16782 12810 1.68x10^ 4 1.28x10^ 4
dim. 40 59228 42446 5.92x10^ 4 4.24x10^ 4
dim. 38 181116 121888 1.81x10^ 5 1.22x10^ 5
dim. 36 492378 311262 4.92x10^ 5 3.11x10^ 5
dim. 34 1210949 718571 1.21x10^ 6 7.19x10^ 5
dim. 32 2729673 1518724 2.73x10^ 6 1.52x10^ 6
dim. 30 5695210 2965537 5.70x10^ 6 2.97x10^ 6
dim. 28 11083379 5388169 1.11x10^ 7 5.39x10^ 6
dim. 26 20241387 9158008 2.02x10^ 7 9.16x10^ 6
dim. 24 34862609 14621222 3.49x10^ 7 1.46x10^ 7
dim. 22 56856340 21993731 5.69x10^ 7 2.20x10^ 7
dim. 20 88092886 31236546 8.81x10^ 7 3.12x10^ 7
dim. 18 130029311 41936425 1.30x10^ 8 4.19x10^ 7
dim. 16 183263256 53233945 1.83x10^ 8 5.32x10^ 7
dim. 14 247098324 63835068 2.47x10^ 8 6.38x10^ 7
dim. 12 319234048 72135724 3.19x10^ 8 7.21x10^ 7
dim. 10 395690620 76456572 3.96x10^ 8 7.65x10^ 7
dim. 8 471046277 75355657 4.71x10^ 8 7.54x10^ 7
dim. 6 539002617 67956340 5.39x10^ 8 6.80x10^ 7
dim. 4 593209277 54206660 5.93x10^ 8 5.42x10^ 7
dim. 2 628208483 34999206 6.28x10^ 8 3.50x10^ 7
dim. 0 640309604 12101121 6.40x10^ 8 1.21x10^ 7