In this experiment, we used the recoilless absorption and emission of the Mössbauer effect coupled with a Doppler shifted emitter to probe the nuclear transitions between the excited $I= 3/2$ state and the ground $I = 1/2$ state of ${}^{57}\mathrm{Fe}$. Three absorbers were studied; we observed the unsplit transition in stainless steel, nuclear Zeeman splitting in enriched ${}^{57}\mathrm{Fe}$, and electric quadrupole splitting in sodium nitroprusside. Using the stainless steel, we obtained a value for the lifetime of the $I = 3/2$ state to be $\tau_{\mathrm{meas}} = 63 \pm 3 \mathrm ns$, a value substantially lower than the literature value of $\tau = 140 \mathrm{ns}$. We determined the dipole moment of the excited state to be $(1.31 \pm 0.04) \times 10^{27} \mathrm{Am}^2$, and the ratio of the magnetic dipole moment in the ground state to that in the excited state was found to be $0.35 \pm 0.01$. The internal magnetic field of the enriched ${}^{57}\mathrm{Fe}$ was calculated to be $186 \pm 4 \mathrm{kG}$, within 3% of the literature value. Finally, we found $Q dE/dz$ in the nitroprusside sample to be $(1.56 \pm 0.02) \times 10^7 \mathrm{Vm}$ and we estimated $dE/dz$ to have a range between $(1.56 \pm 0.02) \times 10^{21} \mathrm{V/m^2}$ and $(1.56 \pm 0.02) \times 10^{22} \mathrm{V/m^2}$.

This abstract is quite nice. The author highlights the main parts of the experiment,—the observation of three effects in three different absorbing samples,—and the key results are listed with uncertainties and placed in context by comparing to literature or expectations.

Is it absolutely clear to someone who has not done the experiment? No. For example, one may still not understand what the Mössbauer effect is (and why it is needed) or what role the Doppler effect plays, but this is close to what we expect for an advanced undergraduate or first-year graduate student and such an abstract would likely receive full credit.

We tested a situation whereby an 810 nm beam was sent through a Mach- Zehnder interferometer with variable path length (by way of piezo-electric crystal). We observed interference at the apertures of the interferometer. Furthermore, we verified that this interference was due to single indivisible photons passing through the interferometer one at a time.

How does this abstract compare with the last one? Hopefully you see that this one could use some work. If we think back to our definition of the abstract as a summary that says something about all parts of the report, we can go step-by-step to find what’s wrong and what can be improved.

The author says “a situation” is being tested and that “interference” is observed, but neither of these statements is expanded upon. The author needs to describe the conditions in which he or she expects interference and (at least briefly) why. They should also clarify what is meant by interference; what data, for example, does the experimenter actually collect and how does that demonstrate that a photon has interfered with itself?

The author gives some specific details (e.g. the light is 810 nm and the interferometer is a Mach-Zehnder type), but they do not give even a general idea of the experimental setup. The emphasis here is inverted; the absolutely necessary information is missing, while the information given is extraneous.

An abstract must, must, must give results. Here, there are no quantitative results and the qualitative results (e.g. the author observes “interference”) are incomplete or misleading. For example, reading the full report shows that interference appears only in certain cases, but not all; this is consistent with expectations and serves to further support the hypothesis. (But again, that hypothesis is not laid out here.)

P. Dubé et al., Phys. Rev. Lett. 112, 173002, 2014.

We report a high-accuracy measurement of the differential static scalar polarizability $\Delta a_0$ of the $5s^2S_{1/2} → 4d^2D_{5/2}$ transition of the ${}^{88}\mathrm{Sr}^+$ ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine $\Delta a_0$ without the need to determine the electric field. $\Delta a_0$ is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the ${}^{88}\mathrm{Sr}^+$ ion clock. The measured value of $\Delta a_0$ is $(4.7938 \pm 0.0071) \times 10^{−40} \mathrm{Jm^2/V^2}$. Taking into account the dynamic correction, the blackbody shift at 300 K is $0.24799 \pm 0.00037 \;\mathrm{Hz}$. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from $2 \times 10^{−17}$ to $8.3 \times 10^{−19}$. The revised total uncertainty of our reference standard is $1.2 \times 10^{−17}$, limited by the blackbody field evaluation. An additional benefit of the low uncertainty of $\Delta a_0$ is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

This example describes a very specific experiment about physics you likely don’t know anything about. (That’s ok!) However, it showcases all the important features that a good abstract should include.

• The quantities measured are introduced. (The authors measure the differential static scalar polarizability of a particular transition which is related to an important parameter called the blackbody radiation frequency shift coefficient.)
• The method is mentioned. (A special trick whereby two phenomenon cancel is used to achieve high accuracy in their measurement.)
• The importance of the quantity is placed in context. (An accurate measurement is critical because this quantity is used as a standard (i.e. in a “clock”) against which other other measurements are compared.)
• The quantitative results are given with uncertainties and discussed.