The nucleus
206
Pb
differs from the doubly magic nucleus
208
Pb
by two missing neutrons. In
208
Pb
most states at
E
x
<
7.4
MeV are described by one-particle one-hole configurations. The lowest ...configurations with a
g
9
/
2
particle and dominant
p
1
/
2
,
f
5
/
2
,
p
3
/
2
holes and admixtures from
f
7
/
2
and a few more configurations build an ensemble of two dozen states at 3.2
<
E
x
<
4.9
MeV. They are described by rather complete orthonormal transformation matrices of two dozen states with spins from 2
-
to 8
-
to configurations. In
206
Pb
a similar ensemble of states is deduced from the analysis of angular distributions measured in 1969 for the
206
Pb
(
p
,
p
′
)
reaction via the
g
9
/
2
IAR in
207
Bi
. An equivalent
208
Pb
(
p
,
p
′
)
experiment was performed in 1968 at the Max–Planck–Institut für Kernphysik at Heidelberg (Germany). New spins are determined for 32 states and 22 levels in
206
Pb
. The comparison to corresponding states in
208
Pb
studied especially in 1982 yields both remarkable similarities and clear differences. Sizeable
g
9
/
2
p
1
/
2
strength found in 4
-
and 5
-
states is interpreted as admixtures of
p
3
/
2
-
2
and
f
5
/
2
-
2
components to the ground state of
206
Pb
with dominant
p
1
/
2
-
2
character. The description of nuclear states by shell model particle-hole configurations in the lead region needs the inclusion of collective excitations at already very low excitation energies. For the two isotopes
206
Pb
and
208
Pb
a rather good agreement of excitation energies and configuration mixing is observed for states at 3.7
<
E
x
<
4.7
MeV.
.
Ten known states in the heavy nucleus
208
Pb at
2
.
6
<
E
x
<
7
.
9
MeV are described by rotating and vibrating tetrahedrons. The
3
-
and
4
+
yrast states are the first members of the rotational ...band. A
2
±
doublet state with the
2
+
yrast state as one member and the newly recognized
2
-
yrast state as the other member, the
1
-
yrast state, and the third
0
+
state are the heads of the three elementary tetrahedral rotating and vibrating bands. The newly recognized state at
E
x
=
4142
keV was assigned spin 2 in 1975 and is suggested to have negative parity by the absent
208
Pb
(
α
,
α
)
excitation. Four more states at
5
.
7
<
E
x
<
7
.
9
MeV are identified as the next members of the three elementary tetrahedral rotating and vibrating bands. The ambiguous spin assignment to the state at
E
x
=
7020
keV is settled with
3
-
, the state at
E
x
=
7137
keV is assigned
4
-
.
Abstract
The nucleus
$$^{206}\mathrm{Pb}$$
206
Pb
differs from the doubly magic nucleus
$$^{208}\mathrm{Pb}$$
208
Pb
by two missing neutrons. In
$$^{208}\mathrm{Pb}$$
208
Pb
most states at
$$E_x< ...7.4$$
E
x
<
7.4
MeV are described by one-particle one-hole configurations. The lowest configurations with a
g
$$_{{ 9}/{2}}$$
9
/
2
particle and dominant
p
$$_{{ 1}/{2}}$$
1
/
2
,
f
$$_{{ 5}/{2}}$$
5
/
2
,
p
$$_{{ 3}/{2}}$$
3
/
2
holes and admixtures from
f
$$_{{ 7}/{2}}$$
7
/
2
and a few more configurations build an ensemble of two dozen states at 3.2
$$<E_x< 4.9$$
<
E
x
<
4.9
MeV. They are described by rather complete orthonormal transformation matrices of two dozen states with spins from 2
$$^-$$
-
to 8
$$^-$$
-
to configurations. In
$$^{206}\mathrm{Pb}$$
206
Pb
a similar ensemble of states is deduced from the analysis of angular distributions measured in 1969 for the
$$^{206}\mathrm{Pb}$$
206
Pb
$$({{{\textit{p}}}, {{\textit{p}}}' })$$
(
p
,
p
′
)
reaction via the
g
$$_{{ 9}/{2}}$$
9
/
2
IAR in
$$^{207}\mathrm{Bi}$$
207
Bi
. An equivalent
$$^{208}\mathrm{Pb}$$
208
Pb
$$({{{\textit{p}}}, {{\textit{p}}}' })$$
(
p
,
p
′
)
experiment was performed in 1968 at the Max–Planck–Institut für Kernphysik at Heidelberg (Germany). New spins are determined for 32 states and 22 levels in
$$^{206}\mathrm{Pb}$$
206
Pb
. The comparison to corresponding states in
$$^{208}\mathrm{Pb}$$
208
Pb
studied especially in 1982 yields both remarkable similarities and clear differences. Sizeable
g
$$_{{ 9}/{2}}$$
9
/
2
p
$$_{{ 1}/{2}}$$
1
/
2
strength found in 4
$$^-$$
-
and 5
$$^-$$
-
states is interpreted as admixtures of
$${{\textit{p}}}{_{{ 3}/{2}}}^{-2}$$
p
3
/
2
-
2
and
$${{\textit{f}}}{_{{ 5}/{2}}}^{-2}$$
f
5
/
2
-
2
components to the ground state of
$$^{206}\mathrm{Pb}$$
206
Pb
with dominant
$${{\textit{p}}}{_{{ 1}/{2}}}^{-2}$$
p
1
/
2
-
2
character. The description of nuclear states by shell model particle-hole configurations in the lead region needs the inclusion of collective excitations at already very low excitation energies. For the two isotopes
$$^{206}\mathrm{Pb}$$
206
Pb
and
$$^{208}\mathrm{Pb}$$
208
Pb
a rather good agreement of excitation energies and configuration mixing is observed for states at 3.7
$$<E_x< 4.7$$
<
E
x
<
4.7
MeV.
Abstract
In the doubly magic nucleus
$$^{208}\mathrm{Pb}$$
208
Pb
states at excitation energies
$$6\,\lesssim \, E_x <7.0$$
6
≲
E
x
<
7.0
MeV populated by the inelastic proton scattering via the ...doublet isobaric analog resonances
g
$$_{{ 7}/{2}}$$
7
/
2
+
d
$$_{{ 3}/{2}}$$
3
/
2
in
$$^{209}\mathrm{Bi}$$
209
Bi
are studied. Sixteen states containing dominant strengths of the configurations
g
$$_{{ 7}/{2}}$$
7
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
g
$$_{{ 7}/{2}}$$
7
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
are newly assigned spins from
$$2^-$$
2
-
to
$$6^-$$
6
-
, among them ten states are newly identified. Amplitudes with relative signs of up to four one-particle one-hole configurations with strengths down to 0.05% are determined in 40 states with spins from 1
$$^-$$
-
to
$$6^-$$
6
-
. Amplitudes of configurations
d
$$_{{ 3}/{2}}$$
3
/
2
p
$$_{{ 1}/{2}}$$
1
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
for fourteen states and amplitudes of
g
$$_{{ 7}/{2}}$$
7
/
2
p
$$_{{ 1}/{2}}$$
1
/
2
,
g
$$_{{ 7}/{2}}$$
7
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
g
$$_{{ 7}/{2}}$$
7
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
for twenty-seven states are determined. Total strengths up to the full strength are found for configurations
d
$$_{{ 3}/{2}}$$
3
/
2
p
$$_{{ 1}/{2}}$$
1
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
d
$$_{{ 3}/{2}}$$
3
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
with spins from
$$1^-$$
1
-
to
$$3^-$$
3
-
and for
g
$$_{{ 7}/{2}}$$
7
/
2
p
$$_{{ 1}/{2}}$$
1
/
2
,
g
$$_{{ 7}/{2}}$$
7
/
2
p
$$_{{ 3}/{2}}$$
3
/
2
,
g
$$_{{ 7}/{2}}$$
7
/
2
f
$$_{{ 5}/{2}}$$
5
/
2
with spins from 1
$$^-$$
-
to
$$6^-$$
6
-
.
Abstract
Structure, spin, and parity of states in
208
Pb at 9 <
E
x
< 17 MeV are explained by the weak coupling of the 3
−
, 4
+
, 6
+
yrast, and the 12
+
yrare states to one-particle one-hole yrast ...and yrare states. The spins of the particle and the hole are coupled in the stretched or nearly stretched mode. The ns-isomerism of three states is shown to derive from the exchange of an intruder hole and the
p
1/2
hole.
Structure, spin, and parity of states in 208Pb at 9 < Ex < 17 MeV are explained by the weak coupling of the 3−, 4+, 6+ yrast, and the 12+ yrare states to one-particle one-hole yrast and yrare states. ...The spins of the particle and the hole are coupled in the stretched or nearly stretched mode. The ns-isomerism of three states is shown to derive from the exchange of an intruder hole and the p1/2 hole.
Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states at higher excitation energy, in regions of high level density. However, it had ...not been possible up to now to observe chaos in the experimental bound energy levels of any single nucleus. In this paper we study the spectral fluctuations of the 208Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in 208Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.
The unidentified TeV source in Cygnus is now confirmed by follow-up observations from 2002 with the HEGRA stereoscopic system of Cherenkov Telescopes. Using all data (1999 to 2002) we confirm this ...new source as steady in flux over the four years of data taking, extended with radius 6.2′ (±$1.2^\prime_{\rm stat}$ ± $0.9^\prime_{\rm sys}$) and exhibiting a hard spectrum with photon index -1.9. It is located in the direction of the dense OB stellar association, Cygnus OB2. Its integral flux above energies $E>1$ TeV amounts to ~5% of the Crab assuming a Gaussian profile for the intrinsic source morphology. There is no obvious counterpart at radio, optical nor X-ray energies, leaving TeV J2032+4130 presently unidentified. Observational parameters of this source are updated here and some astrophysical discussion is provided. Also included are upper limits for a number of other interesting sources in the FoV, including the famous microquasar Cygnus X-3.
The schematic shell model without residual interaction (SSM) assumes the same excitation energy for all spins in each particle-hole configuration multiplet. In
208
Pb, more than forty states are ...known to contain almost the full strength of a single particle-hole configuration. The experimental excitation energy for a state with a certain spin differs from the energy predicted by the SSM by −0.2 to +0.6 MeV. The multiplet splitting is calculated with the surface delta interaction; it corresponds to the diagonal matrix element of the residual interaction in the SSM. For states containing more than 90% strength of a certain configuration and for the centroid of several completely observed configurations, the calculated multiplet splitting often approximates the experimental excitation energy within 30 keV. The strong mixing within some pairs of states containing the full strengths of two configurations is explained.
Abstract
Study question
Does recent mRNA SARS-CoV-2 vaccination effect IVF pregnancy rate?
Summary answer
We observed no influence of mRNA SARS-CoV-2 vaccine on patients’ IVF cycle outcomes; ...vaccination did not change pregnancy rates.
What is known already
Two recent studies showed that the BNT162b2 mRNA SARS-COV-2 vaccine does not appear to have negative effects on oocytes during controlled ovarian stimulation. Assessment of follicular fluid after vaccination (1) concluded that there was no affect on the follicle quality or function. An additional study of 36 patients that underwent IVF both immediately before and immediately after vaccination found no change in ovarian yield or embryo quality (2).
Study design, size, duration
A retrospective case control study including 385 women from January 1, 2021 to May 31st of the same year.
Participants/materials, setting, methods
The study group included patients that received 2 doses of the Pfizer SARS-COV-2 vaccine between 7-180 days prior to starting IVF and without a history of COVID infection. Controls included unvaccinated patients from the same time period and historical age matched patients from our hospital from the same months in prior years. 385 patients under the age of 40 years met the inclusion criteria, 349 in the control and 36 in the vaccinated group.
Main results and the role of chance
Demographic and clinical characteristics were comparable between groups. The pregnancy rate was 33.3% (n = 12) in the vaccinated group vs 31.8% (n = 111) in the control group (p > 0.1). There were no statistically significant differences between the control and vaccine groups with a small non-significant trend to higher pregnancy rates in vaccinated patients: pregnancy rate OR for vaccination group was 1.17 (95% CI 0.56-2.44).
Limitations, reasons for caution
Our study size was small and was observational leaving it open to confounding and selection bias regarding who chose to receive the vaccine and those in high risk groups for COVID infection. Additionally, longterm effect of the vaccine and booster were not assessed.
Wider implications of the findings
We did not observe any effect of this vaccine regimen on IVF outcomes or pregnancy rates. This underscores worldwide data and physiologic reasoning that there should not be significant effects of this COVID vaccine on developing gametes quality and function and is a good option for those trying to conceive.
Trial registration number
LND 0031-21
PDF
