I am in my last semester of Physics and Mathematics and, at the same time, my first semester in a MS in Applied Math (which I will finish in two more semesters) in one of the top universities for physics grad programs. I plan on pursuing a PhD in Physics by Fall 2020 and was wondering what was the best option to do this summer to increase my chances of being accepted in a program at a top university. I plan on applying somewhere else.
One option is looking for a research internship at another university or a national lab. On the other hand, I have been working in several projects at my home university and I am in a collaboration with another university. I have a publication done with a small group and a renowned professor in mathematics, and if I stay this summer I might be able to finish one or two more since I have been working in said projects for a year or more. The important thing is that I want to publish them before I send in my applications for PhD programs this fall. I think there is a considerably smaller chance of publishing if I go to an internship, and I might be able to apply to short programs like two week summer schools while I work here at my university. Furthermore, I already have participated in two summer internships at a Fermilab and Princeton, so I don't know if it makes any difference participating in a third internship, or if it would be better to potentially publish 1 or 2 publications more before I apply to a PhD program.
Summarizing, what do you think is more important: another internship or another (one or two) publication(s)?
Thank you for your opinions!