LimRank
Collection
Datasets and Models for the LimRank paper. • 5 items • Updated
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0 | MassiveDS API | J = 2 state to the predominantly e 3 − wave functions) and are labeled for a given J by F 3 , F 2 , and F 1 starting from the highest to the lowest energy corresponding to J = N − 1, N, N + 1. From the mixing coefficients it is then possible to derive the lifetimes of the interacting levels. Unperturbed lifetimes of th... |
1 | MassiveDS API | two state, in other words, for any operator A, and any physical quantity is calculated by trace, Tr ρA = A 11 ρ 11 + A 22 ρ 22 . Here ρ 11 and ρ 22 are 1/2 for this case of π/2 pulse. There is one thing to be noted here. The excited state in this case is not exactly a simple state. Exactly it consists of combination of... |
2 | MassiveDS API | , n y = 1) will escape through the same leaky 1D level, n x,s , which remains the favoured decay channel as long as it is occupied. Therefore the total probability for one electron to escape from the occupied states with quantum number n x,s is the probability for a single 1D electron with energy E nx,s , multiplied by... |
3 | MassiveDS API | provide ballpark numbers of the lifetimes of different excited states. The lifetime of an electron in an S2 state is typically on the order of 10-15 second. The lifetime of an electron in an S1 state depends on the energy levels involved. For a $$\pi$$-$$\pi$$* system, the lifetimes range from 10-7 to 10-9 second. For ... |
4 | MassiveDS API | Q value, the 2 1∕2 level with a binding energy of = 3727 eV can also contribute to the transition. This level is located above the endpoint by 37 ± 190 eV. Unfortunately, the accuracy of measurement of the Q value does not allow to make an unambiguous conclusion about the position of the 2 1∕2 level relative to the end... |
5 | MassiveDS API | and factored out 1/(10 nm)2. Generally, the energy levels are not degenerate, i.e. all energies are different. However, some energy levels with different quantum numbers coincide, if the lengths along two or three directions are identical or if their ratios are integers. In our cubic QD case, all three lengths are iden... |
6 | MassiveDS API | state [38]. The highest-lying 5d 10 6s S 2 1/2 Pt − bound state, which has a different electron configuration from that of the ground state, was measured to lie 1.275 67(161) eV above the Pt − ground state [39]. Both excited states are expected to be long-lived since E1 transitions to the ground state are forbidden by ... |
7 | MassiveDS API | this state can only decay in a different way: by internal conversion, by emission of 2 photons or by the emission of an e+ e− -pair, if this last is energetically possible. Parity conservation does not permit internal conversion transitions between two levels with J = 0 and opposite parity. The lifetime of excited nucle... |
8 | MassiveDS API | of the coupling as we might expect. Indeed it turns out that g = g 1 + g 2 , where g 1 / h and g 2 /h are the escape rates introduced in the last Section. This comes out of a full quantum mechanical treatment, but we could rationalize it as a consequence of the "uncertainty principle" that requires the product of the l... |
9 | MassiveDS API | # Transition between excited states 1. Nov 3, 2013 ### gildomar 1. The problem statement, all variables and given/known data An atom in an excited state has a lifetime of 1.2 x 10 -8 sec; in a second excited state the lifetime is 2.3 x 10 -8 sec. What is the uncertainty in energy for the photon emitted when an electron... |
10 | MassiveDS API | radiative lifetimes of the excited states. Based on the values in Table II, we choose to consider two suitable initial excited electronic states: 5f 6d 2 at 30223 cm -1 with J = 15/2 and the 7s 2 7p at 31626 cm -1 with J = 1/2. The IC rates for these two configurations are presented in Tables III and IV. The excited st... |
11 | MassiveDS API | # Transition between excited states ## Homework Statement An atom in an excited state has a lifetime of 1.2 x 10 -8 sec; in a second excited state the lifetime is 2.3 x 10 -8 sec. What is the uncertainty in energy for the photon emitted when an electron makes a transition between these two levels? ## Homework Equations... |
12 | MassiveDS API | 5d 9 6s 2 D IV. SUMMARY AND CONCLUSIONS In conclusion, the lifetimes of the two excited states of the Pt − anion are reported. The highest-lying bound excited state in Pt − , 5d 10 6s S 2 1/2 , was found to have an intrinsic lifetime of 2.54 ± 0.10 s, while only a range of 50-200 ms could be estimated for the intrinsic... |
13 | MassiveDS API | This leads to the resonance condition in the form This determines the complex eigenvalues of k 1 = ζ n /L and then the complex eigenenergies E = 2 k 1 2 /(2m 1 ) = 2 ζ n 2 /(2mL 2 ). (The origin of the energy is set at the Fermi energy of the background Al 0.4 Ga 0.6 As. The bottom of the quantum well is at −300meV.) F... |
14 | MassiveDS API | fs at 0.1 eV above E F and 20 fs at 2 eV as well as different lifetimes for excitation of sp-and d-band electrons. [14] Another interesting feature to be studied by 2PPE are image potential states, which were first predicted in 1978 and which are well described by theory. [15] They arise from an electron being trapped ... |
15 | MassiveDS API | the lifetime width is linear in energy E measured from E F , i.e. FWHM w = α|E − E F |. The coefficient α, which phenomenologically represents the intensity of the lifetime of the photo-hole with increasing binding energy, is a parameter which is determined so that the measured spectra are well reproduced. For both com... |
16 | MassiveDS API | \cite{parthey}. They have gotten an accuracy of about $4,2 \times 10^{-14}$ eV (2,466,061,413,187,035(10)Hz, an accuracy of 4 parts in $10^{15}$). The calculation of the energy of the 2S state is a very boring job. However, in order to make a rough estimation, we do not need to find the exact energy of the 2S state, si... |
17 | MassiveDS API | states given by ρ(E) = 1/(E(v f +1 ) − E(v f )). On figure 5, we observe the continuity of the results around the dissociation limit. The lifetime, as well as the relative contribution from bound and continuum states, are presented in table IV. We observe that the lifetime increases with the vibrational number v. We al... |
18 | MassiveDS API | ∼ m H ∼ 10 14 GeV. The lifetime for the H quantum is then F8 For spin-zero φ, one can make the lifetime much larger by applying (1 + bγ 5 ) to ψ ντ in the mixing interaction (after eq. (10)), and letting b approach unity. This can be a reason for the projection, implying parity nonconservation. This is the time t H use... |
19 | MassiveDS API | the state. The cross indicates the energy and lifetime that minimize χ 2 while the white line is the 1-σ contour line. hindered single-particle E2 transition for the decay to the ground state. For example, the E2 decay of a state at 673 keV with a reduced transition probability of 1 W.u. would result in a level lifetim... |
20 | MassiveDS API | 18 C and 20 C respectively. Figure 8 shows the calculated exact eigenvalue of the pairing Hamiltonian for 18 C and 20 C. Experimentally, only one excited state in 18 C is known. It is a (2 + ) state at 1620 keV from the (0 + ) ground state. Considering what we learn in the previous spectra one may place some confidence... |
21 | MassiveDS API | sharply. Of course, ensuring the condition ∆ = 0 demands a much better knowledge of E is than is available today ((3.5 ± 1) eV [68]). For the range 2 ≤ E is ≤ 5 eV theoretical calculations give T1 2 10 min [52], whereas the authors of [68] claim that T1 2 45 hr for E is = 3.5 eV (M1 transition). Taking into account the... |
22 | MassiveDS API | Direct measurement of the 3 d 2 D 3 / 2 to 3 d 2 D 5 / 2 lifetime ratio in a single trapped 40 Ca + We present for the first time a direct measurement of the lifetime ratio between the 3 d 2 D 3 / 2 and 3 d 2 D 5 / 2 metastable states in a single trapped 40Ca+. A high-efficiency quantum state detection technique is ado... |
23 | MassiveDS API | In some instances there are indications that several transitions are not resolved. Even though the values plotted in Fig. 10 display a lot of scatter, the overall trend indicates a monotonically increasing width of the final state lifetime broadening, but not necessarily a quadratic dependency as formulated earlier. Th... |
24 | MassiveDS API | The energy difference between equidistant interaction partners decreases with increasing distance. For the case of Ne 2 pairs these energy differences between the peaks stemming from different interatomic distances are given by: 3 Å, 4 Å 1.20 eV, 4 Å, 5 Å 0.68 eV and 5 Å, 6 Å 0.48 eV. This means that the spectrum... |
25 | MassiveDS API | ground state arising from the 5s 2 5d 2 D term with the higher energies (71,406 and 72,048 cm −1 ) are the more favorable transitions with shorter lifetimes, while the ones from the 5s5p 2 2 D term with the lower energies (58,844 and 59,463 cm −1 ) are much longer lived. Previously this was known only theoretically. Ou... |
26 | MassiveDS API | larger (more than 100 times) than the ones of the E2 transition. The radiative lifetimes of the levels 4d 8 ( 3 F )4f 4 I 15/2 and 4d 8 ( 3 F )4f 4 I 13/2 are extremely large (more than 10 seconds) due to their position in the energy spectra. Although these two levels are relatively very low in the spectra, the level 4... |
27 | MassiveDS API | ≈ 10 78 , the electron number N e ≈ 10 81 , the photon number N tγ ≈ 10 88 , and the phonon number N tp ≈ 10 75 are conserved good quantum numbers as described above. The matter current at the Planck scale, the (V -A) current and the electromagnetic current at the electroweak scale, the baryon current and the proton cu... |
28 | MassiveDS API | = -1.5 eV, E4 = - 0.85 eV Now, from the levels given above, E2 - E4 = 2.55 eV Therefore, quantum numbers of the two levels involved in the emission of these photons are 4 and 2. (c) Change in angular momentum in transition from 4 to 2 will be Here, angular momentum (L) is given by $\dfrac{nh}{2\pi}$, where, n = quantum... |
29 | MassiveDS API | M2 and E3 transitions affect the lifetime of 4d 8 ( 1 D)4f 2 H 9/2 , but no so significantly as the lifetimes of previously discussed levels due to the amount of the M1 and E2 transitions allowed from this level. The radiative lifetimes of other levels with J = 9/2, located higher in the energy spectra than the discuss... |
30 | MassiveDS API | for this factor is the renormalisation of the density of emitted photon states. For a CaF 2 crystal, n = 1.55 at wavelength λ = 159 nm (corresponding E = 7.8 eV), which gives a reduction factor of 3.7 for the lifetime. A more significant lifetime reduction can be connected with electronic bridge and bound internal conv... |
31 | MassiveDS API | to the differences between the initial and final rovibronic states are in the range from 10 meV to 50 meV and are typical for the case under consideration. The mentioned electronic non-adiabatic couplings allow the calculation of the vibrational coupling element between selected states according to Eq. 8. Assuming that... |
32 | MassiveDS API | energy (<300 keV) electrons. At higher energies (>300 keV), the measured lifetimes become smaller than model lifetimes during low AE activity (green solid line), falling in closer agreement with model lifetimes for moderate activity (100 < AE < 300 nT). This behavior is probably partly due to the upper limit of <20 day... |
33 | MassiveDS API | having ℓ ′ = ℓ ± 1 (which themselves mix with states ℓ ′ ± 1). However, m ℓ (or, in atoms with large fine structure splittings like Rb, m j ) remains a good quantum number. This mixing obviously has the potential to impact our lifetime measurements, given the generally much longer lifetimes of the np states than of the... |
34 | MassiveDS API | lifetime τ is bounded by (roughly 95% confidence level) 0.66 × 10 6 s eV 3 /ω 3 ≤ τ ≤ 2.2 × 10 6 s eV 3 /ω 3 . In Fig. 5, the bound is plotted as a function of isomeric transition energy (blue dash-dotted lines). For completeness, the energy ranges from 2.5 eV, which includes the now-rejected value of the transition en... |
35 | MassiveDS API | will be about the same for all of them. | S( k ) | 2 ≈A e −B/ E . Here B=( π 2m /ℏ )( Z−2 )2 e 2 is not an adjustable parameter: and plotting ln | S( k ) | 2 against 1/ E for Polonium212 (which emits α ’s with energy 8.95MeV, and lasts 3× 10 −7 seconds) Thorium232 (4.05MeV α ’s, 1.4× 10 10 years), and several intermedi... |
36 | MassiveDS API | 2S state in atomic hydrogenlike systems is 8.229 Z 6 s −1 (inverse seconds). At Z = 1, this is equivalent to the "famous" value of 1.3 Hz which is nowadays most frequently quoted in the literature. The lifetime of a hydrogenic 2S level is thus 0.1215 Z −6 s. This latter fact has been verified experimentally for ionized... |
37 | MassiveDS API | 10 –6 eV . size 12{ΔE =" 5" "." "3 " times " 10" rSup { size 8{"–25"} } " J " cdot { {"1 eV"} over {1 "." "6 " times " 10" rSup { size 8{"–19"} } " J"} } =" 3" "." "3 " times " 10" rSup { size 8{"–6"} } " eV" "." } {}$ 29.51 Discussion The lifetime of $10−10s10−10s size 12{"10" rSup { size 8{ - "10"} } s} {}$ is typica... |
38 | MassiveDS API | with the recent width of meV derived from measured cross sections in recent collision experiments (Lee et al 1996). The shortness of the time for which exponential decay (ED) holds and the fact that the survival probability, P(t), is still significant at the beginning of the NED, does not allow the rigorous justificati... |
39 | MassiveDS API | 200 eV higher in energy, which makes mixing negligible. 40 To our knowledge, the present spectrum is the first Br KLL Auger spectrum reported in the literature since the work of Erman and coworkers published in 1965. 6 In their work, the 1s À1 core hole in a 79 Br atom was formed by an electron-capture decay of 79 Kr a... |
40 | MassiveDS API | long lifetime of 4 ps for 760 nm (1.63 eV) shown in Fig. 7(b) can be explained by assuming an excited state "Int" lying 1.63 eV above the "def" state. Three electronic levels, "def", "Int", and 3eg can explain the observed asymmetrical delay-time dependence. the valence band top when the bandgap energy is 3.2 eV. Then,... |
41 | MassiveDS API | + 1 and 8 + 1 states are always larger than 6 + 2 and 8 + 2 states, confirming the isomeric nature for the first yarst states of these spins, despite the change of configuration. The 6 + 2 state decays with the M 1 + E2 transition, and the M 1 transition shows a large impact by reducing the half-life from ns to ps. Sim... |
42 | MassiveDS API | two modes estimated above is of order 10 −1 , then the lifetime τ S is of order 10 −37 s (this is an "initial" time interval after hypothetical inflation). The Hubble expansion time scale corresponding to an energy scale of ∼ 10 16 GeV is ∼ 10 −38 s. The S decay thus occurs in a non-equilibrium situation; back-reaction... |
43 | MassiveDS API | and H 2 18 O energy level with quantum numbers K a , K c , ν 1 , ν 2 and ν 3 . On their own, the rigorous quantum numbers from DVR3D do not provide enough information to match with the empirical energy levels from MARVEL. Hence, energy level differences must be used together with this information to match with MARVEL s... |
44 | MassiveDS API | lifetimes of J = 13/2 levels The configuration 4p 6 4d 8 4f has five levels with J = 13/2. The radiative lifetimes of the lowest level 4d 8 ( 3 F )4f 4 I 13/2 are presented in Fig. 5. The lifetimes of this level increase with the Z increasing, because the location of this level in the energy spectrum is going down, i.e... |
45 | MassiveDS API | |1E 2g x2−y2 > is E 2E1u − E 1E2g = 5.75 eV, with corresponding period T 2E1u,1E2g = 719 as. Likewise, the energy gap between states |2E 1u y > and |1A 1g > is E 2E1u − E 1A1g = 14.23 eV, with period T 2E1u,1A1g = 291 as. These two periods are short enough to satisfy condition (47) for two laser pulses with durations τ... |
46 | MassiveDS API | to 20, the solid line results from equation (1) using LS-coupling according to Laughlin [11]. The dashed line shows the present modification of Laughlin's calculations taking into account the splitting between the 3 P 0 and 3 P 1 energy levels [12]. For details see text. increases the predicted lifetimes by factors ran... |
47 | MassiveDS API | t τ , we expect that it decays as e −t/τ 1 − t/τ , where τ is the lifetime given by Fermi's golden rule 1/τ ∼ ρ(E 0 )W 2 , where ρ(E 0 ) is the density of states (per site) of the atomic band at energy E 0 . The lifetime should therefore scale as 1/W 2 . This is indeed what we observe: for example, for E 0 3.087, we fi... |
48 | MassiveDS API | for almost all strong E1 transitions, our radiative rates are accurate to better than 10%. However, for the weaker transitions the accuracy is comparatively poorer. Lifetimes The lifetime τ for a level j is defined as follows: Since this is a measurable parameter, it provides a check on the accuracy of the calculations... |
49 | MassiveDS API | of 0.06-0.1 eV for V Si −As 3 . Similarly to the case of V Si we do not find for V Si − As and V Si − As 2 an energetically favored trapped positron state but just a metastable configuration in disagreement with the experimental trend. The trend in our trapping energies is exactly the opposite; the trapping energy incr... |
50 | MassiveDS API | but we can estimate the order of magnitude in this preliminary assessment, which is considered a 2S → 2P transition: The number of excited atoms or the number of events will be: RN t = 4π 3 χ 2 e 2 I A ′ a 2 0 N t = 1.93 * 10 8 χ 2 N (t/second) (M/eV) (13) where N is the number of populated 2S states and t is the integ... |
51 | MassiveDS API | All one sees are some broadened, weak peaks and gaps superimposed on a broad, continuous density of states. We now analyze the nature of the electronic states for these configurations. We start with the case which has only disorder. In Fig. 6 we plot |G R (k min , k max ; E)| 2 as a function of the energy E, for differ... |
52 | MassiveDS API | remain separated. Figure 12 shows the 6 1 Σ + g radiative lifetimes obtained from the full (Eq. 4) calculation for J = 1 and J = 31, plotted as a function of their vibrational level. The large difference of approximately a factor of three between the J = 1 and J = 31 lifetimes for v = 40 and for v = 100 occurs due to a... |
53 | MassiveDS API | Across all AC sizes (Figure \ref{ac_zz_rel}(d)), S$_3$ lifetimes are never more than 2 ps and higher-energy state lifetimes are within 10-50 fs ($E/E_G >$ 1.5, where $E_G$ is the first excitation energy). In contrast, the S$_3$ lifetime is two orders of magnitude larger for ZZ150 ($\tau^{ZZ150}_{S_3} =$ 19.9 ps) and fu... |
54 | MassiveDS API | = 0f(z) SI I SOj valid solutionf() + f(-t) 2f' (2t) = 2 Q2 Consider continuously differentiable functions f R R such that for every & > 0, the following relation holds: ay Ta? JIf f dr dy dz = (f(a) + sin(a) - 1) () 122 + y D(a} where D(a) = {(1,y,2) : 22+y + 22 < &',lyl < 43} Which of the following is true? f(0) + f'(... |
55 | MassiveDS API | π = 9/2 − assignment is a better solution from the angular correlation fits. It also presents the longest lifetime, a newly measured 1170(300) fs, with respect to the other levels discussed in this section. An enhanced B(E2) value of 27 +15 −9 W.u. for the 689.6 keV E2 transition to the 5/2 − one-phonon state suggests ... |
56 | MassiveDS API | supports an infinite number of image states exibiting the well-known Rydberg series form: E n =−͑13.6/ 16n 2 ͓͒͑⑀ −1͒ / ͑⑀ +1͔͒ eV, where n =1,2,3,... is the principal quantum number. Since E n ϳ 1 / n 2 , the states with higher n have weaker binding energies. This series converges to the vacuum level. The electrons ar... |
57 | MassiveDS API | possible to obtain precise values of either E1 matrix elements or transition strengths from the measured lifetimes due to association of many transition probabilities with these quantities. However, the 4P states are the first two excited states which decay to the ground state only via one allowed transition each. Ther... |
58 | MassiveDS API | the 2 → 1 transition would result in the emission of −8 eV − (−12 eV) = 4 eV. Therefore, if the atom is initially in the _n_ = 3 state, it could emit photons of energy 3 eV, 4 eV, or 7 eV. 7. **D** The energy of the _n_ th level is given by the equation _E_ _n_ = _E_ 1/ _n_ 2, where _E_ 1 is the ground-state energy. Th... |
59 | MassiveDS API | at the Heidelberg EBIT consisted in the lifetime measurement of the first-excited energy level of boronlike Ar XIV. The forbidden transition at 441.26 nm arising from this level was used to monitor its depopulation (cf. Fig. 3). The high light collection efficiency of our setup allowed us to observe evidence of a small... |
60 | MassiveDS API | a shift in the B 2 Σ + potential minimum marked by the hollow dot in Fig. 7(a). To minimise the effect of errors in r e , the calculated B 2 Σ + state is shifted by this value prior to determination of the decay channels. All the tabulated theoretical values are performed following this transformation and the equivalen... |
61 | MassiveDS API | GENERAL: See also Table 8.3 [Table of Energy Levels] (in PDF or PS). Theory: See (1955HE1E, 1956KU1A, 1956PE1A, 1957BI1C, 1957FR1B, 1958WI1E). Recent Q-values are 93.7 ± 0.9 keV (1957CO59: 9Be(p, d)8Be), 90 ± 5 keV (1955TR03: 11B(p, α)8Be): the weighted mean of all measurements is 94.1 ± 0.7 keV (1957VA11). The width o... |
62 | MassiveDS API | energy E(v, J) lower than U J (R J ) has a finite lifetime before it will be decomposed due to a quantum tunneling effect. These states are called quasibound states and formally belong to the continuum. What is important is that during their lifetimes they can be regarded as bound states. When the energy E(v, J) exceed... |
63 | MassiveDS API | presented in Wong et al. (2017), see Fig. 5. Due to the change in the model and consequently the wavefunctions, the Einstein-A coefficients between the states of X 2 Π as well as the corresponding lifetimes have also changed. The energies of the lower rovibronic states (v ≤ 29 and J ≤ 99.5) of X 2 Π were replaced with ... |
64 | MassiveDS API | instance for small screenings ξ = 0.5 ) the energy E 10 goes to zero, while E 1,±1 -to minus infinity. This means that at strong disorder and finite screening, our 2D excitons are more stable for higher values of orbital quantum number m. Our numerical analysis shows that this effect realizes for higher excited states ... |
65 | MassiveDS API | + ions, where a decoherence-free entangled state of two ions in the electronic 2 D 5/2 manifold was created to suppress ambient noise 4,5 . The relatively short 1.2 s radiative lifetime of the 2 D 5/2 state in Ca + and the requirement for high fidelity quantum gates limit the scalability and, ultimately, the sensitivit... |
66 | MassiveDS API | horizon of our universe. Besides, for a free particle with mass m 0 , its energy also assumes discrete values E n = n 2 h 2 32m 0 R 2 U . For instance, the minimum energy is E 1 ≈ 10 −72 eV for free electrons, which is much smaller than the minimum energy of photons 9 . It is interesting to see whether this tiny discre... |
67 | MassiveDS API | the energy of the 2 + state in 136 Gd to be 165 keV. Figure 9 shows the expected half-life as a function of Q p . It is expected that for lifetimes longer than the limit marked by the grey line, beta-decay will dominate [46]. C. Theoretical Uncertainties It should be emphasized that our method contains no adjustable pa... |
68 | MassiveDS API | −4 (eV) 2 , the condition (34) (or (32)), with n = 2, leads to ∆ξ (2) reach as deep as ∼ 10 −24 . Alternatively, one may wish to relinquish this high sensitivity of ∆ξ (n) for the sake of probing deviations from E 2 = p 2 + m 2 that are suppressed by m P at a much higher order. As an extreme example, one can imagine a ... |
69 | MassiveDS API | alleged lifetime of 10 ns is extracted from τ = Q/ω, which is the classical ring-down time of a classical oscillator with frequency ω/2π and quality factor Q. This is not the implied lifetime T 1 of a quantum system with discrete energy levels. Furthermore, T 1 of different energy levels in an atom is different for dif... |
70 | MassiveDS API | 38 . Here, the center of gravity of the experimental scaled lifetime (≈ 25 fs eV 2 ) is close to the GW +T curve for energies higher than ∼ 0.7 eV. Below this value, towards E F , the experimental lifetime goes down faster than the GW + T one. However, the experimentally observed less rapid increase in the lifetime tow... |
71 | MassiveDS API | b 3 Σ + , v = 5 system. To verify the fraction of triplet character, f b5 (F, n, ±), of the hyperfine levels, lifetime measurements are performed. The lifetime τ of a certain hyperfine level characterized by the quantum number F, the counting integer n and the parity, is given by and largely differs for the different h... |
72 | MassiveDS API | from Table 4. Lifetimes for the calculated states are displayed in Fig. 5. For the (1 − , 0) state, the lifetime is infinite within the present description. The large difference between the lifetimes of the (2 + , 0) state and, for example, the (0 + , 1) state is essentially due to the factor (E i − E f ) 5 in expressi... |
73 | MassiveDS API | an order of magnitude larger than the empirical value E A 1 emp ≈ 6 × 10 −4 extracted from the 5700 a half life of 14 C. We also find that the matrix element E A 1 depends on the energy of the first excited 1 + state in 14 N. For the three different cutoffs Λ χ = 450, 500, 550 MeV this excited 1 + state is at 5.69, 4.4... |
74 | MassiveDS API | measured. In similarity with the other $N=89$ isotones, this first excited state can be considered part of the g.s. band built on the $\nu5/2[523]$ configuration. \textbf{The 175.3-keV level \soutthick{$(1/2^-_1)$} $(3/2^-_1)$:} The measured lifetime for this state is surprisingly short. Assuming a pure $E2$ character ... |
75 | MassiveDS API | 1, n α is the initial occupancy of the shell α, and the emitted electron has energy ε. A configuration interaction calculation using the atomic code AMBiT [39] indicates initial shell occupancies for the uranium ground state of 7s 1.79 6d 1.09 3/2 6d 0.12 5/2 5f 2.73 5/2 5f 0.27 7/2 . With these values of n α , we calc... |
76 | MassiveDS API | Q, and filling the levels as follows: a) First we list the (E nx , τ nx ), in order of increasing n x (and therefore of increasing energy and decreasing lifetime.) This list is truncated at an n x = n x,max whose lifetime is less than 0.01 sec. b) Next we form a list of 2D levels (n x , n y ) by choosing those for whic... |
77 | MassiveDS API | 3, 4, 5 are shown, n r = 2 having the longest lifetime and n r = 5 having the shortest. The dashed line shows the ratio t 1 /(ν 1 U ) which should be less than unity for the expression to be valid. As a comparison, the resulting lifetime obtained in the wideband limit Eq. (20) is also shown as the dash-dotted line. The... |
78 | MassiveDS API | over {1 "." "6 " times " 10" rSup { size 8{"–19"} } " J"} } =" 3" "." "3 " times " 10" rSup { size 8{"–6"} } " eV" "." } {} (12) Discussion The lifetime of 1010s1010s size 12{"10" rSup { size 8{ - "10"} } s} {} is typical of excited states in atoms—on human time scales, they quickly emit their stored energy. An uncerta... |
79 | MassiveDS API | significant. The larger the Yukawa coupling y 1 and y 2 , the larger the difference. In these cases, both λ(t) and λ(t) have no minimum for energy scale below the Planck scale. The energy scale of bounce, Λ B , is chosen as the Planck scale for these two cases. We note that the positive sign of λ − λ shown in Fig 4 mea... |
80 | MassiveDS API | 1 / 40 =8.99E9 ( N-m 2 / C 2 ) The energy increment required to create such a pair includes the mass energy, the potential energy, and the kinetic energy of revolution: E = 2mc 2e 2 / 40r + ½ m 2 r 2 = 2mc 2 -½ e 2 / 40r Inspect these two equations for an e+e-mass of 1.02 MeV and a dipole frequency range from th... |
81 | MassiveDS API | lifetimes have been calculated to lie in the range of a couple of seconds (Table 2), which should be much easier to measure than the hour-range lifetimes of the 3s 2 3p 3 2 D o 3/2,5/2 levels. Figure 5 reveals that the scatter of the predictions is sizeable in this case, too. The latest data point is from a data base w... |
82 | MassiveDS API | 0 set by the long range asymptotic behaviour of the van der Waals interaction (see Fig. 1). This trend is confirmed by our direct calculations of the molecular life- (9) and (12), respectively. The magnitude of the bare state lifetime τres is indicated by the dotted line. For the purpose of comparison, we have slightly... |
83 | MassiveDS API | Relativistic configuration interaction calculations of lifetimes of Si− 3p3 bound excited states Relativistic configuration interaction lifetimes of Si− 3p3 2D3/2, 2P1/2 and 2D5/2 states are calculated (using M1 and E2 length gauge transition probabilities) to be 162 s, 23.6 s and 27.3 h, respectively. Detailed analysi... |
84 | MassiveDS API | states have lifetimes that scale as 1/β 2 , where β is the size of the asymmetric perturbation. To get lifetimes in SI units, the conversion is (1 unit of time in atomic units = 2.42 * 10 −17 sec). In an experiment, this lattice could experience small noisy perturbations and still have impressively long-lived states in... |
85 | MassiveDS API | of the 5 − state. However, the contribution of the configuration involving ν1h 9 2 in both the ground state and the 5 − state is calculated to be less than 1%. In the present work, the transition probability for the above mentioned 5 − level to the 2 − ground state was calculated by considering the resultant 33 keV γ t... |
86 | MassiveDS API | He+ 2p state lifetime by a quenching-asymmetry measurement. An interference asymmetry in the angular distribution of the Ly-α quenching radiation emitted by He + ions in the metastable 2s 1/2 state is measured to high precision to obtain the lifetime of the 2p 1/2 state. The derived lifetime of (0.997 17±0.00075) ×10 -... |
87 | MassiveDS API | than 5 keV. Some discrepancies can be explained at low energies due to the low efficiency of the small E1 events. Distributions of ∆T are shown in Fig. 5 (d) together with results from exponential fits for only large ∆T events. This is because the two-pulse selection strongly suppress small ∆T events. Only events with ... |
88 | MassiveDS API | Be-like ion, and E = E γ 1 + E γ 2 is the 3 P 0 → 1 S 0 transition energy shared by the two photons γ 1 and γ 2 given in eV. The theoretical E1M1-lifetimes obtained from equation 1 by using theoretical excitation energies E [12] are shown by the (red) solid line in figure 2. For Xe 50+ one obtains a lifetime τ E1M 1 of... |
89 | MassiveDS API | element term in our case. However, we do not see the QPI pattern to be present apart from these two energy scales, unless a large lifetime broadening is used in the calculation to smear out the quasiparticle states. (b1)-(b2) Corresponding experimental QPI data at these two energy scales for electron doped pnictide at ... |
90 | MassiveDS API | 0.14 T/s. The long dotted lines indicate the minima of P th whereas the short dotted lines indicate the minima of P −10,10 . by The probability for a spin to pass into the excited level m can be estimated by τ −1 m e −E10,m/kBT , where E 10,m is the energy gap between the levels 10 and m, and τ m is the lifetime of the... |
91 | MassiveDS API | in Table 1 we obtain the lowest order values for multiphonon relaxation of 8, 7, 6, and 5 for lead The measured lifetime for the 4 I 13/2 upper laser state of erbium decreases, whereas lifetime for the 5 D 0 state of europium increases with increasing phonon energy in glass matrices. Moreover, the change of the 4 I 13/... |
92 | MassiveDS API | total energy of the two-particle quantum system, obtaining Let us also remark that the total BH energy E = − M 2 is negative and different from the BH inert mass M. Thus, by using Eq. (51), one gets from Eq. (127) Remarkably, Eq. (129) is exactly the same Eq. (53). Thus, one can use again Eq. (51) in order to re-obtain... |
93 | MassiveDS API | most important transition determining the lifetime is ν2p 1/2 → π2p 3/2 . In the presence of pairing correlations, the energy of the corresponding 2qp excitation is increased and the lifetime becomes longer for increasing values of f iv . This transition remains the dominant one also in the case of 80-84 Ni, but is les... |
94 | MassiveDS API | 29\,eV respectively. Therefore the expected energy of the isomer transition (7.8\,eV) is above the ionization energy of the neutral Thorium atom.}. In the \emph{Th$^{3+}$ ion} for $E=7.6$\,eV the expected lifetime is the same as in a bare nucleus described above, if the valence electron is in the ground $5f_{5/2}$ stat... |
95 | MassiveDS API | and so it has a lifetime of 2.2 × 10 6 seconds, or ∼25 days, which is several orders of magnitude longer than any of the other levels. IV. SUMMARY AND CONCLUSION We have calculated energies, g-factors, and lifetimes of several low-lying atomic levels in Lr + . A striking agreement between the calculated FSCC and CI+MBP... |
96 | MassiveDS API | the fitting procedure. In general, the agreement with the data is better for the states with even J values, while the calculated theoretical energy levels with odd J values appear systematically above the experimental excitation energies. We carry out a more detailed comparison for both the energies and E2 properties i... |
97 | MassiveDS API | of the remaining atoms, N e , by optically pumping 5s5p 3 P 0 , 3 P 2 → 5s5p 3 P 1 with light resonant on the 5s5p 3 P 0 , 3 P 2 ↔ 5s6s 3 S 1 transitions at 679 nm and 707 nm. Atoms then rapidly decay to the ground state, via the 21 µs lived 5s5p 3 P 1 [23], where they are subsequently imaged with 461 nm light. We note... |
98 | MassiveDS API | [43]. When m ≥ ω, the time-delay factor Ω = 0, the quantum system will be locked up in the initial state. This is due to the fact that the entanglement generation and degradation is via the the excitation and de-excitation of the two-level systems, which are possible only when m < ω. This is the selection rule for quan... |
99 | MassiveDS API | a nuclear clock of extremely high stability, due to an expected high resilience against external influences and a radiative lifetime in the range of minutes to hours [7][8][9][10]. It is generally assumed that direct nuclear laser excitation of 229m Th requires a considerably improved knowledge of the isomeric transiti... |
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