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Erratum to “Weak decay of Λ hypernuclei: quark versus mesons” [Nucl. Phys. A 669 (2000) 331–350]
Nuclear Physics A 678 (2000) 455–456 www.elsevier.nl/locate/npe
Erratum
Erratum to “Weak decay of Λ hypernuclei: quark versus mesons” [Nucl. Phys. A 669 (2000) 331–350] ✩ Kenji Sasaki ∗ , Takashi Inoue, Makoto Oka We have found an error in the K exchange potential, so that the K exchange amplitudes, fp and fn (3 S1 → 3P1 ) change the sign. Accordingly, Tables 1 and 2 of the original paper should be replaced by the new ones. The main consequence is that the π and K exchanges interfere constructively and thus enhance fp and fn . In the nuclear matter calculation we see that Γp = 1.431ΓΛ(0.674), Γn = 1.025ΓΛ(0.021), Γn /Γp = 0.716(0.031) for the “π (soft) + K + DQ” mechanism. The values in the parentheses are original values with error. This indicates that Γn , Γn /Γp , and PV/PC ratio are all enhanced strongly. Note that we also see that the total decay rate (Γtot ' 2.5ΓΛ ) is larger than the heavy hypernucleus data even with the soft form factor for the π exchange. It is possible that the short range ΛN and NN correlations in the nuclear medium are not sufficiently strong in the present calculation. For light hypernuclei, similarly to nuclear matter, we see large enhancement of the total decay rates and the Γn /Γp ratios. Now the results using the soft form factor for the pion exchange are all consistent with the current light hypernuclear data. Remember that the old value of the Γn /Γp ratio for 5Λ He is about 0.2. In conclusion, we see a great improvement of the Γn /Γp ratio due to the contribution of the K exchange and the DQ process. The K exchange reduces the strong tensor transition of the π exchange, reducing Γp , while it enhances Γn through fn . DQ enhances both Γp and Γn resulting “π + K + DQ” results are in good agreement with experimental data for light hypernuclei. We acknowledge Dr. Assumpta Parreño for communications regarding this error. ✩
PII of original article: S0375-9474(99)00427-3
∗ Corresponding author.
E-mail address: [email protected] (K. Sasaki). 0375-9474/00/$ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 0 ) 0 0 3 5 6 - 0
456
K. Sasaki et al. / Nuclear Physics A 678 (2000) 455–456
Table 1 Nonmesonic decay rates of Λ in nuclear matter with realistic short-range correlation (in units of ΓΛ ). The “all” includes π , K, η, ρ, ω, and K ∗ meson exchange Total
Γp
Γn
Γn /Γp
PV/PC
π +K
DP hard DP soft no-f.f.
1.759 1.216 2.068
1.300 0.850 1.424
0.459 0.365 0.644
0.353 0.430 0.452
1.594 1.841 2.140
all
DP hard DP soft no-f.f.
2.444 1.906 2.863
1.828 1.363 2.077
0.616 0.543 0.786
0.337 0.398 0.379
2.618 2.818 5.538
DQ + π + K
DP hard DP soft
3.145 2.456
1.970 1.431
1.176 1.025
0.597 0.716
3.578 4.811
DQ + all
DP hard DP soft
3.974 3.288
2.570 2.016
1.404 1.273
0.546 0.631
5.206 6.312
Table 2 Nonmesonic decay rates of each hypernuclei. DP (soft) is used
5 He Λ
π +K π + K + DQ EXP[21] EXP[25]
4 He Λ
π +K π + K + DQ EXP[25]
4H Λ
π +K π + K + DQ EXP[25]
Total
Γp
Γn
Γn /Γp
0.302 0.519
0.209 0.305
0.094 0.214
0.450 0.701
0.41 ± 0.14 0.50 ± 0.07
0.21 ± 0.07 0.17 ± 0.04
0.20 ± 0.11 0.33 ± 0.04
0.93 ± 0.55 1.97 ± 0.67
0.156 0.218
0.147 0.214
0.009 0.004
0.065 0.017
0.19 ± 0.04
0.15 ± 0.02
0.04 ± 0.02
0.27 ± 0.14
0.069 0.184
0.005 0.030
0.065 0.154
13.508 5.088
0.15±0.13
–
–
–
Erratum
Erratum to “Weak decay of Λ hypernuclei: quark versus mesons” [Nucl. Phys. A 669 (2000) 331–350] ✩ Kenji Sasaki ∗ , Takashi Inoue, Makoto Oka We have found an error in the K exchange potential, so that the K exchange amplitudes, fp and fn (3 S1 → 3P1 ) change the sign. Accordingly, Tables 1 and 2 of the original paper should be replaced by the new ones. The main consequence is that the π and K exchanges interfere constructively and thus enhance fp and fn . In the nuclear matter calculation we see that Γp = 1.431ΓΛ(0.674), Γn = 1.025ΓΛ(0.021), Γn /Γp = 0.716(0.031) for the “π (soft) + K + DQ” mechanism. The values in the parentheses are original values with error. This indicates that Γn , Γn /Γp , and PV/PC ratio are all enhanced strongly. Note that we also see that the total decay rate (Γtot ' 2.5ΓΛ ) is larger than the heavy hypernucleus data even with the soft form factor for the π exchange. It is possible that the short range ΛN and NN correlations in the nuclear medium are not sufficiently strong in the present calculation. For light hypernuclei, similarly to nuclear matter, we see large enhancement of the total decay rates and the Γn /Γp ratios. Now the results using the soft form factor for the pion exchange are all consistent with the current light hypernuclear data. Remember that the old value of the Γn /Γp ratio for 5Λ He is about 0.2. In conclusion, we see a great improvement of the Γn /Γp ratio due to the contribution of the K exchange and the DQ process. The K exchange reduces the strong tensor transition of the π exchange, reducing Γp , while it enhances Γn through fn . DQ enhances both Γp and Γn resulting “π + K + DQ” results are in good agreement with experimental data for light hypernuclei. We acknowledge Dr. Assumpta Parreño for communications regarding this error. ✩
PII of original article: S0375-9474(99)00427-3
∗ Corresponding author.
E-mail address: [email protected] (K. Sasaki). 0375-9474/00/$ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 0 ) 0 0 3 5 6 - 0
456
K. Sasaki et al. / Nuclear Physics A 678 (2000) 455–456
Table 1 Nonmesonic decay rates of Λ in nuclear matter with realistic short-range correlation (in units of ΓΛ ). The “all” includes π , K, η, ρ, ω, and K ∗ meson exchange Total
Γp
Γn
Γn /Γp
PV/PC
π +K
DP hard DP soft no-f.f.
1.759 1.216 2.068
1.300 0.850 1.424
0.459 0.365 0.644
0.353 0.430 0.452
1.594 1.841 2.140
all
DP hard DP soft no-f.f.
2.444 1.906 2.863
1.828 1.363 2.077
0.616 0.543 0.786
0.337 0.398 0.379
2.618 2.818 5.538
DQ + π + K
DP hard DP soft
3.145 2.456
1.970 1.431
1.176 1.025
0.597 0.716
3.578 4.811
DQ + all
DP hard DP soft
3.974 3.288
2.570 2.016
1.404 1.273
0.546 0.631
5.206 6.312
Table 2 Nonmesonic decay rates of each hypernuclei. DP (soft) is used
5 He Λ
π +K π + K + DQ EXP[21] EXP[25]
4 He Λ
π +K π + K + DQ EXP[25]
4H Λ
π +K π + K + DQ EXP[25]
Total
Γp
Γn
Γn /Γp
0.302 0.519
0.209 0.305
0.094 0.214
0.450 0.701
0.41 ± 0.14 0.50 ± 0.07
0.21 ± 0.07 0.17 ± 0.04
0.20 ± 0.11 0.33 ± 0.04
0.93 ± 0.55 1.97 ± 0.67
0.156 0.218
0.147 0.214
0.009 0.004
0.065 0.017
0.19 ± 0.04
0.15 ± 0.02
0.04 ± 0.02
0.27 ± 0.14
0.069 0.184
0.005 0.030
0.065 0.154
13.508 5.088
0.15±0.13
–
–
–