Measuring the cross section of the ${}^{15}\mathrm{N}{(\alpha ,\gamma )}^{19}\mathrm{F}$ reaction using a single-fluid bubble chamber

${}^{15}\mathrm{N}{(\alpha ,\gamma )}^{19}\mathrm{F}$ is believed to be the primary means of stellar nucleosynthesis of fluorine. Here, we present the use of a single-fluid bubble chamber to measure the cross section of the time-inverse photodissociation reaction. The method benefits from a luminosity increase of several orders of magnitude due to the use of a thicker liquid target—when compared to thin films or gas targets—and from the reciprocity theorem. We discuss the results of an experiment at the Thomas Jefferson National Accelerator Facility, where the cross section of the photodisintegration process ${}^{19}\mathrm{F}(\gamma , \alpha ){}^{15}\mathrm{N}$ was measured by bombarding a superheated fluid of ${\mathrm{C}}_3{\mathrm{F}}_8$ with bremsstrahlung $\gamma$ rays produced by impinging a 4–5.5 MeV electron beam on a Cu radiator. From the photodissociation yield the cross section was extracted by performing a convolution with a Monte Carlo–generated $\gamma$-ray beam spectrum. The measurement produced a cross section that was then time inverted using the reciprocity theorem. The cross section for the ${}^{15}\mathrm{N}(\alpha ,\gamma ){}^{19}\mathrm{F}$ reaction was determined down to a value in the range of hundreds of picobarns. With further improvements of the experimental setup the technique could potentially push cross section measurements down to the single picobarn range.

Figure 1

Phase diagram (pressure vs temperature) of ${\mathrm{C}}_3{\mathrm{F}}_8$, the active target fluid used in this experiment. The red line shows the region covered in the fiducial area bombarded by the bremsstrahlung beam. This line crosses the phase boundary and creates a superheated liquid which can lead to bubble formation. The blue line represents a cooler region of the glass vessel, such as in the stem of the glass cell. Being at a lower temperature, the liquid does not cross the phase boundary and therefore, does not lead to bubble formation.

Figure 2

Schematic of the bubble chamber used in the experiment. The $\gamma$-ray beam impinges on the detector from the left. The ${\mathrm{C}}_3{\mathrm{F}}_8$ is located in a glass vessel with a long neck that extends down to the region of the hydraulic pressure control system. The temperature is regulated by a mineral oil that surrounds the glass vessel. There is a temperature gradient between the upper region of the glass vessel and the lower region around the glass stem. See text for details.

Figure 3

Stopping power $\mathrm{d}E/\mathrm{d}x$ vs. energy of various ion species moving in the ${\mathrm{C}}_3{\mathrm{F}}_8$ superheated liquid computed using srim [26]. The formation of a protobubble that will grow into an macroscopic (observable) bubble will depend on the amount of superheat in the liquid. The detector becomes active as the pressure drops. An ion moving into the superheated liquid needs to fulfill two conditions to form a macroscopic bubble: the first condition is to be able to deposit enough energy into the active liquid. The dotted horizontal line represents a model [27] for the minimum stopping power (energy deposition per unit length) necessary to induce the formation of an observable bubble. The second condition requires the ion to have enough kinetic energy to form a macroscopic bubble. The vertical solid line is the critical kinetic energy. An ion will trigger the detector when both conditions are met. The region to the right of the vertical solid line and above the dotted line represents the window of detection. The solid line box represents the typical energy range of the recoiling ${}^{15}\mathrm{N}$.

Figure 4

The bubble chamber experiment in the injector tunnel at Jefferson Lab. The electron beam comes in from the left on the bubble spectrometer line. Down the beamline, the electron beam hits the copper radiator. Bremsstrahlung $\gamma$ rays produced at the radiator enter the pressure vessel through a copper collimator. Additional collimation is provided by a tungsten insert and copper entrance flange (see Fig. 2). Not shown is the additional lead shielding placed around the copper radiator during the experimental runs. Inside the steel pressure vessel (illuminated by a green LED) is the glass cell (which holds the active fluid).

Figure 5

Bubble distributions resulting from AmBe neutron source with activity $A$ and at a distance $\mathrm{\Delta }d$ from the pressure vessel (a), from cosmic rays (b), and from bremsstrahlung beams produced from electron beams with current $I$ and energies of 4.0 MeV (c), and 5.351 MeV with approximate cross section of the ${}^{15}\mathrm{N}(\alpha ,\gamma ){}^{19}\mathrm{F}$ reaction for reference (d). The bremsstrahlung beam enters from the left. The vertical and horizontal axes are given in pixels (px), with the position of the bubbles recorded from the CMOS camera. A scale has been added to the first subplot, with 70 px on the CMOS sensor corresponding to 1 cm in the plane of the glass cell. At the second highest energy point (d), corresponding to the electron beam energy closest to the strong ${}^{19}\mathrm{F}$ resonance at $E_x=5.337$ MeV, the bubbles resulting from the $\gamma$-ray beam form a defined fiducial region (solid black line). This region is used for all energies. Below this fiducial region an equally sized “background” region (dashed black line) is used for background subtraction. See text for details.

Figure 6

Effect of refraction on the location of the bubbles from background events at the glass surface occurring in an angular region covering a range of ${30}^{\circ }$ viewed from the top of the glass vessel. Background events from the ${}^{10}\mathrm{B}{(n,\alpha )}^7\mathrm{Li}$ reaction originating at two regions, along (green) and perpendicular (red) to the incoming beam together with refraction effects lead to an enhancement of the events at the entrance and exit of the $\gamma$-ray beam.

Figure 7

Cross sections of the three $(\gamma ,n)$ reactions, multiplied by the natural abundance of each isotope, which can contribute to the beam induced background of the experiment as a function of the $\gamma$-ray energy $E_{\gamma }$. The threshold of each reaction are denoted by the vertical dashed lines. The solid green and blue curves are interpolations to guide the eye. Over the energy ranges of this experiment, the neutron background predominately comes from ${}^2\mathrm{H}(\gamma ,n)$ with ${}^{13}\mathrm{C}(\gamma ,n)$ becoming important at higher energies. See text for details.

Figure 8

Distribution of events measured in the bubble chamber at various bombarding energies using a bremsstrahlung beam produced from an electron beam with energies of $T_e$. The bremsstrahlung beam enters from the left. The electron currents $I$ as well as the estimated cross sections of the ${}^{15}\mathrm{N}(\alpha ,\gamma ){}^{19}\mathrm{F}$ reaction at these energies are included. The approximate run time of each distribution shown is 1 h.

Figure 9

Experimental yield defined by Eq. (3). The black dots represent the central values from the weighted averaging with horizontal bars for the measured spread in the electron beam energy. The hatched area is the 68% confidence limit from the MC calculation. The interpolation of the hatched fill along with the upper and lower lines which bound the fill is only to guide the eye. The dashed red lines are the theoretical yield curve from a model (described in Appendix pp2) which includes the effect of the dominant background resulting from ${}^2\mathrm{H}(\gamma ,n){}^1\mathrm{H}$.

Figure 10

Bremsstrahlung spectra inside the glass cell from the geant4 simulation of the electron beam at $T_e=4.813$ MeV. The dashed vertical line marks where the two simulations described in Sec. 5c are stitched together. The high statistics region resulting from a simulation of ${10}^{11}$ electrons using an energy cut at 3.8 MeV. The low statistics region resulting from a simulation of ${10}^9$ electrons using an energy cut at 2.2 MeV. The lower statistics data set is scaled and combined to the high statistics set near the ${}^{19}\mathrm{F}(\gamma ,\alpha ){}^{15}\mathrm{N}$ reaction threshold (matched over a range extending around 100 keV to the left of the red dashed vertical line). The result shown here is then scaled to match the total beam charge of the $T_e=4.813$ MeV experimental run listed in Table 2.

Figure 11

A 2D $\gamma$-ray distribution inside the glass cell from a geant4 simulation of the $T_e=4.813$ MeV electron beam using ${10}^9$ electrons. The origin has been centered relative to the center of the copper radiator. The vertical walls of the glass cell are outside the range of the figure (in this coordinate system, having an $x$ position at approximately $+18$ and $-18$ mm).

Figure 12

Probability density function (PDF) for bremsstrahlung $\gamma$ rays resulting from an electron beam with the energies listed in Table 1 to photodisintegrate ${}^{19}\mathrm{F}$, based on the calculated cross section described in Appendix pp2. The PDF for $T_e=5.351$ and 5.398 MeV have been scaled down by a factor of 10. From the peak of each PDF one determines the excitation energy at which the corresponding value of the cross section was measured. The FWHM of each PDF are listed in Table 3. One can see that even with the broad bremsstrahlung spectrum used, the cross section falls off sufficiently fast at low energies. The energy range of the $\gamma$ rays which contribute to the yield resembles the shape of a peak.

Figure 13

Comparison of experimental cross sections taken from Fig. 12 of Ugalde et al. 2013 [7] as green crosses and this work as blue circular dots with the theoretical Breit-Wigner cross section using partial widths from Wilmes et al. [13] as solid red curve and partial widths from Di Leva et al. [14] as dashed blue curve for the ${}^{15}\mathrm{N}(\alpha ,\gamma ){}^{19}\mathrm{F}$ reaction. The hatch fill of the Breit-Wigner curves comes from varying the $\alpha$-particle width of the $E_R=5.337$ MeV resonance by the $1\sigma$ limits measured in each respective paper. The horizontal black dash-dotted line represents the $1\sigma$ limits on the beam background of the current bubble chamber setup.

Figure 14

The 0L and spectrometer lines are coplanar in the horizontal plane. The 2D and 5D lines form $-{30}^{\circ }$ and ${25}^{\circ }$ angles, respectively, with the straight ahead 0L line. The bubble chamber was installed on the 5D line. Setting and measuring the electron beam characteristics for the experiment used the 0L, 2D, and 5D lines.

Figure 15

Considering the dipole from Fig. 14, the electron beam traverses a circular arc, ${\ell }_{\text{arc}}=\rho \alpha (\rho$ is known as the radius of curvature), through the dipole field, $\mathbf{B}$. A convenient way to model a dipole is to use an ideal uniform dipole field, $B$, of finite extent, known as the effective length, ${\ell }_{\text{eff}}=\text{BDL}/B$ (=12.88 cm for our dipole). From the geometry, ${\ell }_{\text{eff}}=\rho sin\alpha$, and the relation between the curved orbit and the effective length of the dipole is then ${\ell }_{\text{arc}}/{\ell }_{\text{eff}}=\alpha /sin\alpha$.

Figure 16

Dipole settings ${\left[\text{BDL}\right]}_{2\text{D}}$ versus ${\left[\text{BDL}\right]}_{5\text{D}}$ and linear least-squares fit of Eq. (A2).