I. INTRODUCTION

Nucleosynthesis during a thermonuclear runaway in an oxygen-neon (ONe) nova remains not fully understood. ONe novae have been identified as thermonuclear runaways on the surfaces of O-Ne-Mg enriched white dwarfs, which develop after the carbon-burning phase during stellar evolution. The reaction path above the seed nucleus 20 Ne is characterized by the hot NeNa and MgAl cycles, which produce longlived radioactive nuclei 22 Na and 26 Al, respectively [1][2][3]. Extensive measurements of the proton capture reactions in the higher mass range have demonstrated that the reaction path above 28 Si and 32 S follows the line of stability towards 40 Ca [4][5][6][7][8][9][10]. At temperatures typical of novae, 0.2 < T 9 < 0.7 (T 9 = 10 9 K), the reaction rates are too slow to compete with the β + decays of nuclei along the path, and back-processing reactions 31 P(p, α) 28 Si, 35 Cl(p, α) 32 S, and 39 K(p, α) 36 Ar are hindered by the reduced penetrability of α particles through the Coulomb barrier of their respective high-Z compound nuclei [4]. The endpoint of the reaction path has been linked with the proton capture on the doubly magic 40 Ca nucleus. The strength of the 40 Ca(p, γ ) 41 Sc reaction is the key to understanding the endpoint of the nucleosynthesis pattern for ONe novae. While it was shown that ONe nova ejecta are dominated by medium mass abundances in the Al to Si range, observations such as those of Cygni V1974 indicate the presence of Fe material, which might be explained by the reaction path bridging into higher mass ranges [11,12]. However, these interpretations still carry large uncertainties since the physical processes in the ejecta environments are not well understood.

From the nuclear structure point of view, there has been a lot of interest in the structure of the 41 Ca - 41 Sc mirror nuclei [13][14][15]. 40 Ca is a doubly magic nuclide, having closed shells for both protons and neutrons. Observation of low-lying excited states in the 41 Ca - 41 Sc mirror nuclei, with one nucleon bound to 40 Ca, is of significance for the independent particle model.

At novae temperatures, the 40 Ca(p, γ ) 41 Sc reaction is governed by a low energy resonance at E lab R = 647 keV. Because of the double closed shell nature of 40 Ca, the Q value for proton capture is low, Q = 1085 keV [16], and the lowest energy resonance corresponds to the first excited, and proton unbound, state in the 41 Sc compound nucleus at E x = 1716.48 keV J π = 3/2 -(see Fig. 1). The E lab R = 1842 keV resonance serves as a normalization standard for nuclear reaction experiments [17] because of its pronounced resonance strength. This resonance corresponds to the seventh excited state in the 41 Sc compound nucleus at E x = 2882.47 keV J π = 7/2 + ; see Fig. 1. The strengths of both resonances have been measured multiple times in the past (see Sec. II for details on previous works). However, existing uncertainties and discrepancies in the reported strength values of the E lab R = 647 and 1842 keV resonances in the 40 Ca(p, γ ) 41 Sc reaction have highlighted the need for a more precise measurement. In this study, we present a new direct and absolute measurement of the strengths of these lowenergy resonances.

The structure of the paper is as follows. Section II reviews the current literature on these two resonances. Section III describes our experimental setup, details of the target properties, and the experimental procedure. In Sec. IV, we present the analysis methods and the results obtained from our measurements. Section V uses these results to calculate the thermonuclear reaction rate and discusses its implications for the production and destruction of 40 Ca. Finally, Sec. VI summarizes our findings and outlines potential future research directions.

II. LITERATURE REVIEW

The resonance strength, ωγ , is defined as [18]

Here, p , γ , and are the proton partial width, photon partial width, and total width, respectively. The statistical factor, ω, is related to the angular momentum J 1 , J 2 , and J of the projectile, target, and resonance, respectively. For the 40 Ca(p, γ ) 41 Sc reaction, the projectile is a proton (J 1 = 1/2) and the target is 40 Ca (J 2 = 0), and thus (2J 1 + 1)(2J 2 + 1) = 2. In previous studies (as discussed in the following subsections), S(p, γ ), is often used and is defined as S(p, γ ) = (2J + 1) p γ / , and for the 40 Ca(p, γ ) 41 Sc reaction we have

A.

The strength of the 1842 keV resonance has been measured several times in the past. The first absolute measurement was conducted by Butler [19] in 1961 using CaO targets, and inbeam γ spectrometry and the 41 Sc (t 1/2 = 596.3 ms [16]) β + counting technique. The subsequent measurement was performed by Engelbertink and Endt [20], where the strength was measured relative to 31 P(p, γ ) 32 S, 32 S(p, γ ) 33 Cl resonances using Ca 3 (PO 4 ) 2 and CaSO 4 targets. In the following measurements by Youngblood et al. [21] and Kozub et al. [22], an absolute strength was measured using metallic Ca targets. In 1979, Paine and Sargood [23] measured the strength relative to the 27 Al(p, γ ) 28 Si resonance. After nearly three decades, an absolute strength measurement of the 1842 keV resonance was carried out by Robertson et al. [24] using metallic Ca targets. All these measurements reported strength values that agreed within 1σ with each other. The latest measurement by Schmidt et al. [25] reports a value that is 37% (equivalent to 3.5σ ) higher than the previous literature values. In that study, Ca(OH) 2 targets were used, and both absolute and relative [relative to 40 Ca(α, γ ) 44 Ti] measurements were reported. All the existing strength values for the 1842 keV resonance have been summarized in Table I.

TABLE I. Strength of the E lab R = 1842 keV resonance from literature and present work. ωγ (eV) Year Reference Technique 0.15 +0.15 -0.08 1961 Butler [19] in-beam γ spectrometry and 41 Sc β + counting 0.13 ± 0.02 1966 Engelbertink and Endt [20] relative to 31 P(p, γ ) 32 S, 32 S(p, γ ) 33 Cl resonances 0.193 ± 0.047 1968 Youngblood et al. [21] 41 Sc β + counting 0.14 ± 0.02 1977 Kozub et al. [22] in-beam γ spectrometry 0.140 ± 0.025 1979 Paine and Sargood [23] relative to 27 Al(p, γ ) 28 Si resonance 0.14 ± 0.02 2012 Robertson et al. [24] in-beam γ spectrometry 0.192 ± 0.017 2014 Schmidt et al. [25] both absolute and relative to 40 Ca(α, γ ) 44 Ti 0.148 ± 0.006 stat ± 0.013 syst 2024 present work in-beam γ spectrometry TABLE II. Strength of the E lab R = 647 keV resonance from direct experimental measurements from literature and present work. ωγ (meV) Year Reference Technique 2.94 +2.94 -1.47 a 1961 Butler [19] in-beam γ spectrometry and 41 Sc β + counting 2.5 ± 0.6 a 1968 Youngblood et al. [21] 41 Sc β + counting 2.51 ± 0.09 stat ± 0.22 syst 2024 present work in-beam γ spectrometry a Resonance strength is measured relative to the strength of the 1842 keV resonance. B. E lab R = 647 keV resonance

The strength of the 647 keV resonance has been measured only twice. The strength was measured for the first time by Butler [19] in 1961 with a factor of 2 uncertainty either way. In that study, CaO targets were used, and in-beam γ -ray spectrometry and the 41 Sc β + counting technique were employed. A subsequent measurement was performed by Youngblood et al. [21] in 1968, using the same β + counting technique with metallic Ca targets. In both measurements, the strength was measured relative to the 1842 keV resonance in the same 40 Ca(p, γ ) 41 Sc reaction. These direct experimental measurements are summarized in Table II.

Since the strength value of the 647 keV resonance was measured relative to that of the 1842 keV resonance, and, because the strength values of the 1842 keV resonance have changed over the years (as shown in Table I), various strength values for the 647 keV resonance have been reported in different compilation papers. In the first compilation paper in 1967, Endt and Van der Leun [26] reported a value of S(p, γ ) = 5.2 ± 1.6 meV and ωγ = 2.6 ± 0.8 meV, obtained using the strength of the 647 keV resonance from Butler [19] as normalized to the yield of the 1842 keV resonance from Youngblood et al. [27]. In 1973, in a subsequent evaluation and compilation paper, Endt and Van der Leun [29] reported a value of S(p, γ ) = 5 meV and ωγ = 2.5 based on the Youngblood et al. [21] measurement. However, in a later evaluation in 1978, Endt and Van der Leun [29] revised the value to S(p, γ ) = 3 meV and ωγ = 1.5 meV, normalizing it to the yield of the 1842 keV resonance from Engelbertink and Endt [20]. Finally, in a 1990 compilation by Endt [30], the strength was further updated to S(p, γ ) = 1.8 meV and ωγ = 0.9 meV based on the yield of the 1842 keV resonance from Paine and Sargood [23]. It is important to note that the reported value of S(p, γ ) in Endt [30] is erroneously listed; the correct value should be S(p, γ ) = 3.6 meV and ωγ = 1.8 meV. This correct value was used in the compilation by Iliadis et al. [31] in 2001, where a value of ωγ = 1.8 ± 0.2 meV was provided. However, the error in this value is understated, as it does not account for the uncertainty in the 1842 keV resonance. The correct value should therefore be ωγ = 1.80 ± 0.45 meV. In the latest NNDC compilation by Nesaraja and McCutchan [16], the erroneous value from Endt [30] was still considered. Table III summarizes all the existing strength values for the 647 keV resonance from various compilations.

As is evident from previous studies, there are uncertainties and discrepancies in the strengths of the E lab R = 647 and 1842 keV resonances in 40 Ca(p, γ ) 41 Sc, which prompted the need for a new experiment.

III. EXPERIMENT

A. Experimental setup

The experiment was performed using the St. ANA 5 MV pelletron accelerator at the Institute for Structure and Nuclear Astrophysics (ISNAP) at the University of Notre Dame, USA [32]. The 5 MV accelerator delivered proton beams with an intensity limited to < 5 µA on Ca target. The energy calibration of the accelerator was performed by measuring the well-known resonance in the 27 Al(p, γ ) 28 Si reaction at E lab R = 992 keV [33]. The beam was sent through a 90 • analyzing magnet before being transported to the experimental

TABLE III. Strength of the E lab R = 647 keV resonance from compilations. S(p, γ ) (meV) ωγ (meV) Year Reference Comment 5.2 ± 1.6 2.6 ± 0.8 1967 Endt and Van der Leun [26] value of the strength of the 647 keV resonance from Butler [19] as normalized to the yield of the 1842 keV resonance from Youngblood et al. [27]. 5 2.5 1973 Endt and Van der Leun [28] value of the strength of the 647 keV resonance from Youngblood et al. [21]. 3 1.5 1978 Endt and Van der Leun [29] as normalized to the yield of the 1842 keV resonance from Engelbertink and Endt [20]. 1.8 a 0.9 1990 Endt [30] as normalized to the yield of the 1842 keV resonance from Paine and Sargood [23]. -1.8 ± 0.2 b 2001 Iliadis et al. [31] P. M. Endt, private communication (1998). 1.8 0.9 2016 Nesaraja and McCutchan [16] as normalized to the yield of the 1842 keV resonance from Paine and Sargood [23]. a This value is erroneously listed as S(p, γ ) instead of ωγ in Endt [30]. b The correct value should be 1.8 ± 0.45 meV (see text). target station, providing a beam energy uncertainty of ±1 keV at 1 MeV. The beam was defocused and wobbled over an area of approximately 1 cm 2 on the target to mitigate target degradation and reduce the effects of target inhomogeneities. The target was mounted at the end of the beamline as shown in Fig. 2.

A high purity germanium (HPGe) detector, an n-type coaxial type EGC 100-260-R from Canberra [34], was used to measure γ rays from the 40 Ca(p, γ ) 41 Sc reaction. This HPGe detector was quoted to have an efficiency of 100% relative to a 3 in. × 3 in. NaI detector, with an energy resolution of ≈ 0.26% at 1332 keV. The detector was placed at 0 • relative to the beam direction on a movable stand, directly behind the target as shown in Fig. 2. The electrically insulated target chamber acted as a Faraday cup, which was used for the integration of the beam current. To limit carbon buildup on the target, a cold trap was mounted that consisted of a copper tube, cooled to liquid nitrogen temperature, and placed inside the beam line. The copper tube extended to within a few millimeters of the target surface. The cold trap was electrically insulated and biased to -500 V to suppress secondary electrons. The target was water-cooled to reduce damage resulting from beam-induced power deposition.

B. Target preparation

A fresh Ca target was prepared by using the vacuum evaporation technique. A 0.25 mm thick Ta sheet was used as the target backing. It was sequentially cleaned with acetone, ethyl alcohol, and semiconductor-grade isopropyl alcohol, with ultrasonication applied at each step, followed by drying in an Ar flow. The sheet was then annealed under a vacuum of 1 × 10 -6 Torr using direct current heating to remove surface contamination. Ca metal (natural enrichment) was subsequently evaporated at a pressure of 8 × 10 -6 Torr. The distance between the Ca source boat and the tantalum sheet was set at 20 cm to ensure uniform deposition. Real-time monitoring of the deposition was performed using Au-coated quartz crystals, with thickness measurements recorded by a monitor. The evaporation rate was kept at 0.5 µg/min. After the evaporation process, the target was allowed to cool for 30 minutes, followed by introducing high-purity Ar gas into the evaporator. Finally, the targets were transferred to the beamline using an Ar-filled glove bag to prevent oxidation.

C. Experimental procedure

First, the energy calibration of the accelerator was performed by measuring the front edge of the thick-target yield curve from the E lab R = 992 keV resonance in the 27 Al(p, γ ) 28 Si reaction [33,35]. A full thick-target resonance scan was performed to obtain the thickness of the Al target. Using the thick-target yield information of Antilla et al. [33], the detection efficiencies, η, were determined at various γ energies, E γ , by taking a long run on the plateau of the resonance with the HPGe detector in far geometry [d = 22.8( 2) cm], where d is the distance between the target holder and end cap of the HPGe detector, in order to make the effects of summing negligible.

In the second step, the freshly produced 40 In the third step, the E lab R = 647 keV resonance was measured. A resonance scan was performed by observing the 1716.5 keV primary γ -ray transition BR = 100%) with the HPGe in close geometry (d = 1.7 cm). As done in the previous step, to determine the resonance strength, measurement runs, typically lasting 8-10 min, were taken on the plateau of the resonance scan curve (achieving <4% statistical uncertainty in the counts of the 1716.5 keV γ ray).

In the last step, detection efficiency runs were carried out using a 137 Cs source (a single γ -ray line source) placed on the target holder. Then a few long runs were taken with the HPGe in close (d = 1.7 cm) and far geometry (d = 22.8 cm) so that the far geometry efficiency curve could be scaled to the close geometry.

IV. ANALYSIS

A. Resonance scan

Resonance scans show the γ yield from the resonance integrated over the target thickness. The scans reflect both the distribution of the target material as well as the resonance strength, which corresponds to the yield on top of the scan [36].

Scans for both resonances were performed by changing the proton beam energy and observing the yield of the most intense primary γ -ray transition: E γ = 1716. Resonance scan plot for the E lab R = 647 keV resonance using the 1716.5 keV primary γ -ray transition. The target thickness obtained using Eq. ( 4) is E lab = 102.2(3) keV at 647 keV. and 4. Each of these scans was fit with an empirical function [37]

where h is the height of the plateau, and E lab R , E , and E lab are the resonance energy, beam energy, and target thickness in the laboratory frame, respectively. δ L and δ R are two empirical parameters that account for the beam straggling at the target boundaries in the rising and falling front, respectively.

B. Detection efficiency

To determine the absolute detection efficiencies, η, for various γ -ray energies, a long run was taken on the plateau of the E lab R = 992 keV resonance in the 27 Al(p, γ ) 28 Si reaction, with the HPGe detector positioned in far geometry (d = 22.8 cm). The far geometry was chosen to minimize summing effects. To evaluate η, counts for the specific γ -ray were determined from the experimental spectrum and then normalized to the expected counts, based on the average yield of (1.08 ± 0.06) × 10 -9 1778.9 keV γ -rays per incident proton, as reported by Keinonen and Anttila [35], and Paine and Resonance scan plot for the E lab R = 1842 keV resonance using the 2883.1 keV primary γ -ray transition. The target thickness obtained using Eq. ( 4) is E lab = 52.0(2) keV at 1842 keV. Sargood [23], and the branching ratios provided in Table I of Antilla et al. [33]. The η values obtained for different E γ were then fitted using the function [38] η(E γ ) = e a+b log(E γ )+c log 2 (E γ )+d log 3 (E γ ) ,

where a, b, c, and d are fitting parameters. Using the above function and the obtained parameters from the fit, η(E γ ) was calculated for a given γ -ray energy at d = 22.8 cm. However, for the strength measurements of the two resonances in the 40 Ca(p, γ ) 41 Sc reaction, runs were taken with the detector positioned at close geometry (d = 1.7 cm). To obtain η(E γ ) (d = 1.7 cm), η(E γ ) (d = 22.8 cm) was scaled by a factor of η close /η far = 22.04 ± 0.24. To calculate η close /η far , multiple long runs were performed using a 137 Cs source with the HPGe detector in close (1.7 cm) and far (22.8 cm) geometry. The 137 Cs source emits a single primary γ ray at 661 keV, and thus, there is no summing effect at any distance d. The efficiency curve is shown in Fig. 5.

C. Angular distributions

The primary γ -rays from the 40 Ca(p, γ ) 41 Sc reaction are emitted with intrinsic angular distributions. The angular distributions can be described in terms of a series of Legendre polynomials as

where, a n , are Legendre coefficients, which can be calculated from the spin and angular momenta vector coupling with the γ -ray transition multipolarity and, Q n , are attenuation factors, which depend on the geometry of the specific detector target arrangement [39]. Because the resonances under consideration are narrow, only even order Legendre coefficients are needed and the expansion is truncated at second order because higher orders are expected to be negligible.

For the E lab R = 1842 keV resonance, angular distribution Legendre coefficients for the ground state transition were taken from Kozub et al. [22]; a weighted average of a 2 = 0.507 ± 0.017. No measurement exists for the angular distribution of the E lab R = 647 keV resonance's (J π = 3/2 -)

TABLE IV. Systematic uncertainty for the absolute determination of the resonance strength ωγ . Uncertainty source Contribution Beam current 3% Stopping power 1.7% γ -ray detection efficiency 6.5% γ -ray angular distribution 5% Total systematic uncertainty 8.9%

ground state (J π = 7/2 -) transition, so its theoretical angular distribution was used. The lowest order multipolarity, E 2 in this case, was assumed to dominate, where the next lowest order multipolarity was M3. A theoretical value of a 2 = 0.143 was calculated using the azure2 code [40].

The Q n coefficients can be calculated analytically from the geometry as [39]

where

where r is the detector crystal radius (r = 4 cm), l is the length of the detector crystal (l = 8.5 cm), and D is the distance from the target to the detectors' face in close geometry [D = 1.7(1) + 0.5 1 = 2.2(1) cm]. The uncertainty in the Q n coefficients is dominated by the uncertainty in D, which is 5%.

D. Resonance strength

For the thick target yield condition [36], the resonance strength, ωγ , is determined from the experimental yield, Y , and is given by

where λ r , is the de Broglie wavelength at the resonance energy in the center-of-mass frame, r is the effective stopping power at the resonance energy in the laboratory frame (calculated using srim-2013 [41]), and m and M are the projectile and target masses, respectively. For both the resonances reported in this work, resonance width, , is significantly smaller than the energy loss (in the center-of-mass frame) ( E c.m. ) and hence the thick-target condition is well satisfied. Yield is calculated using

where N is the sum of the counts from all primary γ rays, e is the elementary charge (e = 1.602 × 10 -19 C), q is the total accumulated charge from the incident proton beam, and η and W (θ ) are the detection efficiency and angular distribution of the emitted γ , respectively. 1 The distance from the crystal to the front of the detector cap. For the 647 keV resonance, the Y was calculated using the counts from the only primary γ transition, E γ = 1716.5 keV (BR = 100%). For the 1842 keV resonance, the Y was calculated using the counts from the most intense primary γ transition, E γ = 2883.1 keV, corrected for its branching ratio (BR = 99.92%). No γ -ray peak was observed from the E γ = 786 keV primary γ -ray transition (BR = 0.08%) in the experimental data. The resonance strengths of the two low-energy resonances evaluated using the thick target approach are ωγ (E lab R = 647 keV) = (2.51 ± 0.09 stat ± 0.22 syst ) meV and ωγ (E lab R = 1842 keV) = (0.148 ± 0.006 stat ± 0.013 syst ) eV (see also Tables I and II). The total uncertainty is calculated as the square root of the sum of the squares of the systematic and statistical uncertainties. The strength of these resonances has been measured with a total uncertainty of <10% in the present work. The dominant uncertainty contribution comes from systematic uncertainty, with its various components listed in Table IV.

For the E lab R = 647 keV resonance, the present measurement reaffirms the previous direct measurements by Butler [19] and Youngblood et al. [21], with the uncertainty of our value reduced by a factor of 2.5. For the E lab R = 1842 keV resonance, our measured value is consistent with the literature but shows a deviation of 2σ from the value reported by Schmidt et al. [25] foot_0 as shown in Fig. 6.

V. THERMONUCLEAR REACTION RATE

The total thermonuclear reaction rate of the 40 Ca(p, γ ) 41 Sc reaction was calculated by summing both nonresonant and resonant contributions,

where N A σ v NR is the nonresonant contribution and N A σ v R is the resonant contribution. To evaluate N A σ v R , all eight 3 resonances mentioned in Iliadis et al. [43] were considered. The resonant reaction rate was calculated assuming the resonances to be narrow and isolated using [18]

where μ is the reduced mass in atomic mass unit u, ωγ is the resonance strength in eV, and E c.m. R is the resonance energy in the center-of-mass frame in keV.

The nonresonant component of the reaction rate can be expressed in terms of the S factor. It has been shown that the S factor for the direct capture process to the 7/2 -ground state in 41 Sc is characterized by a d → f E 1 transition, which is weak compared to the resonance contributions except at very low temperatures [3,44]. In the first calculation by 3 The E lab R = 1036 and 1363 keV resonances have ωγ = 0 [43], and thus only six resonances contribute to the N A σ v R calculations. Reaction rate ratio of various resonant and non-resonant contributions to the total reaction rate for the 40 Ca(p, γ ) 41 Sc reaction as a function of temperature. In the novae temperature range, 0.2 < T 9 < 0.7, E lab R = 647 keV resonance dominates the total reaction rate.

Wiescher and Görres [3], S(E 0 ) = 64 keV b was used. The factor was calculated in the framework of a direct capture Wood-Saxon potential model and normalized to experimental values taken at higher energies [44]. A similar approach by Iliadis et al. [31] revealed a considerably smaller value of S(E 0 ) = 19.2 keV b. In the present work, we calculate the nonresonant term S(E 0 ) using the R-matrix azure2 code [40], which uses the external capture model [45][46][47][48]. Our new calculation yields a value of S(E 0 ) = 96(15) keV b, which is normalized to the higher energy experimental data of Terrasi et al. [44]. Using S(E 0 ) = 96(15) keV b, the corresponding reaction rate was calculated using the following equation [18]:

where

Figure 7 displays the total reaction rate along with the rate components from various resonances and direct capture. The reaction rates for the E lab R = 647 and 1842 keV resonances are calculated using the strengths measured in this work.

TABLE V. Resonance parameters for the first and seventh excited states in the 40 Ca(p, γ ) 41 Sc reaction. E x E lab R p γ ωγ (present work) (keV) (keV) J π (eV) (eV) (eV) 1716.48(8) [16,49] 647.28(5) [49] 3/2 -[21] 2.72 [3] a 0.0013(4) [27] 2.51(24) × 10 -3b 2882.47(8) [16,49] 1842.66(14) [49] 7/2 + [22] 0.090(11) [22] 0.058(7) [22] 0.148(14) b 0.085 (10) [49] 0.060(7) [49] a In Ref. [3], p is calculated from the spectroscopic factor C 2 S = 0.8. b ωγ value measured in the present work is consistent with that calculated using the level parameters from previous works listed in the above Table at the 1σ level. The total reaction rate of the 40 Ca(p, γ ) 41 Sc reaction in the temperature range 0.1 < T 9 < 10 is provided in Table I in the Supplemental Material [50].

The different parameters for the 647 and 1842 keV resonances are summarized in Table V. It should be noted that both the ground state of 41 Sc as well as the first excited state at 1716.48 keV, which corresponds to the 647 keV resonance, are characterized by large single particle spectroscopic factors, which underline their configuration as f p-shell single-particle states coupled to a closed 40 Ca core.

Figure 8 shows the resonant and non-resonant reaction contributions. The dominant contribution over the entire temperature of nova burning comes from the resonance at 647 keV. Higher energy resonance levels, with resonance strengths taken from the compilation by Iliadis et al. [43] are negligible except for the J π = 7/2 + resonance at 1842 keV (E x = 2882.47 keV), which dominates the reaction rate at higher temperatures T 9 > 4 GK, well beyond the peak characteristic temperatures of novae. At temperatures below T 9 = 0.15, the direct capture dominates the reaction rate as highlighted in Fig. 8.

An important aspect of the discussion is the role of the 40 Ca(p, γ ) 41 Sc reaction for the reaction flow in a hot ONe nova environment. The comparison of the recently determined 40 Ca feeding reaction 39 K(p, γ ) 40 Ca [10] and the here analyzed 40 Ca depletion via the 40 Ca(p, γ ) 41 Sc reaction, as shown in Fig. 9, clearly demonstrates that the feeding reaction is between one and two orders of magnitude stronger than its depletion.

Assuming equilibrium in the reaction flow, this translates into a temperature dependent 40 Ca / 39 K abundance ratio as approximated by the following equation 40

This clearly suggests that the double-closed shell nucleus 40 Ca represents a major impedance in the reaction flow, causing an accumulation of 40 Ca. This effect may be further enhanced by the low Q value of the 40 Ca(p, γ ) 41 Sc reaction, Q = 1085 keV, which at high temperature condition leads to substantial inverse photodisintegration of 41 Sc, causing 40 Ca to become an important waiting point at higher temperatures than anticipated at nova conditions.

A leakage of 40 Ca via the 40 Ca(p, γ ) 41 Sc reaction is unlikely during the short period of sufficiently high temperature conditions during the thermonuclear runaway of the nova event, which lasts for only about 10 to 100 days [51]. Figure 10 shows the survival time, τ , versus temperature:

with X H ≈ 0.5 as the mass fraction of hydrogen and ρ ≈ 10 3 g/cm 3 being the density. 4 Figure 10 shows the corresponding timing conditions for the reaction conditions necessary to branch the 40 Ca waiting point. It indicates that at certain temperature conditions, not too low to warrant a sufficient 40 Ca leak and not too high to reduce the inverse 41 Sc photodisintegration rate, a few percent of the accumulated 40 Ca may be processed further into the Ti, Mn, Fe range. Detailed network simulations are in preparation to determine the temperature conditions necessary for a leakage process.

VI. SUMMARY AND OUTLOOK

The strength of the two low-energy resonances at E lab R = 647 and 1842 keV in the 40 Ca(p, γ ) 41 Sc reaction have been measured with < 10% total uncertainty using the 5U accelerator at the Nuclear Science Laboratory at the University of Notre Dame.

For the E lab R = 647 keV resonance, our measured strength value agrees within 1σ uncertainty with the measured values reported in Butler [19] and Youngblood et al. [21], where our uncertainty is reduced by a factor of 2.5. Our measurement represents the first absolute measurement of the strength of the 647 keV resonance.

For the E lab R = 1842 keV resonance, our measured strength agrees within 1σ uncertainty with the measured values as reported by Butler [19], Engelbertink and Endt [20], Youngblood et al. [21], Kozub et al. [22], Paine and Sargood [23], and Robertson et al. [24], but deviates from the value reported by Schmidt et al. [25] by 2σ . Our measured value can be used as a normalization point for future precision experiments on 40 Ca targets.

Our results suggest that 40 Ca is a strong waiting point for the reaction flow in the thermonuclear runaway of nova events. However, more detailed simulations in the framework of a mesa based nova model [2] are in progress to explore the possibility of 40 Ca leakage towards the higher mass range of f p-shell nuclei, feeding material in the Mn to Fe range.